# This file is part of xrayutilities.
#
# xrayutilities is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program; if not, see <http://www.gnu.org/licenses/>.
#
# Copyright (c) 2017-2023 Dominik Kriegner <dominik.kriegner@gmail.com>
__all__ = ["RangeDict", "eqhkl_default", "eqhkl_custom", "wp"]
[docs]
class RangeDict(dict):
"""Dictionary type which uses range as keys"""
def __getitem__(self, item):
if not isinstance(item, range):
for key in self:
if item in key:
return self[key]
return super().__getitem__(item)
return super().__getitem__(item)
eqhkl_default = RangeDict({
range(1, 2): lambda h, k, l: ((h, k, l), ),
range(2, 3): lambda h, k, l: ((-h, -k, -l), (h, k, l)),
range(3, 6): lambda h, k, l: ((h, k, l), (-h, k, -l)),
range(6, 10): lambda h, k, l: ((h, -k, l), (h, k, l)),
range(10, 16):
lambda h, k, l: ((-h, -k, -l), (h, k, l), (-h, k, -l), (h, -k, l)),
range(16, 25):
lambda h, k, l: ((-h, -k, l), (h, k, l), (h, -k, -l), (-h, k, -l)),
range(25, 47):
lambda h, k, l: ((-h, -k, l), (h, -k, l), (h, k, l), (-h, k, l)),
range(47, 75):
lambda h, k, l: ((h, k, l), (-h, k, -l), (-h, -k, l), (-h, -k, -l),
(h, -k, -l), (h, -k, l), (-h, k, l), (h, k, -l)),
range(75, 81):
lambda h, k, l: ((-h, -k, l), (k, -h, l), (h, k, l), (-k, h, l)),
range(81, 83):
lambda h, k, l: ((-h, -k, l), (-k, h, -l), (h, k, l), (k, -h, -l)),
range(83, 89):
lambda h, k, l: ((h, k, l), (k, -h, l), (-k, h, -l), (-h, -k, l),
(-h, -k, -l), (-k, h, l), (k, -h, -l), (h, k, -l)),
range(89, 99):
lambda h, k, l: ((h, k, l), (-h, k, -l), (k, -h, l), (-k, -h, -l),
(k, h, -l), (-h, -k, l), (h, -k, -l), (-k, h, l)),
range(99, 111):
lambda h, k, l: ((h, k, l), (k, -h, l), (k, h, l), (-h, -k, l),
(h, -k, l), (-h, k, l), (-k, h, l), (-k, -h, l)),
range(115, 121):
lambda h, k, l: ((h, k, l), (-k, -h, -l), (-k, h, -l), (k, h, -l),
(-h, -k, l), (h, -k, l), (-h, k, l), (k, -h, -l)),
(111, 112, 113, 114, 121, 122):
lambda h, k, l: ((h, k, l), (-h, k, -l), (-k, h, -l), (k, h, l),
(-h, -k, l), (h, -k, -l), (k, -h, -l), (-k, -h, l)),
range(123, 143):
lambda h, k, l: ((h, k, l), (-h, k, -l), (k, -h, l), (-k, -h, -l),
(k, h, -l), (-k, h, -l), (k, h, l), (-h, -k, l),
(h, -k, -l), (-h, -k, -l), (h, -k, l), (-h, k, l),
(-k, h, l), (k, -h, -l), (-k, -h, l), (h, k, -l)),
range(143, 147): lambda h, k, l: ((h, k, l), (k, -h-k, l), (-h-k, h, l)),
range(147, 149):
lambda h, k, l: ((h, k, l), (h+k, -h, -l), (k, -h-k, l),
(-h, -k, -l), (-k, h+k, -l), (-h-k, h, l)),
(149, 151, 153):
lambda h, k, l: ((h, k, l), (k, -h-k, l), (-k, -h, -l),
(-h, h+k, -l), (-h-k, h, l), (h+k, -k, -l)),
(150, 152, 154, 155):
lambda h, k, l: ((h, k, l), (k, -h-k, l), (-h-k, k, -l),
(h, -h-k, -l), (k, h, -l), (-h-k, h, l)),
(157, 159):
lambda h, k, l: ((h, k, l), (k, -h-k, l), (k, h, l), (-h-k, k, l),
(-h-k, h, l), (h, -h-k, l)),
(156, 158, 160, 161):
lambda h, k, l: ((h, k, l), (k, -h-k, l), (h+k, -k, l),
(-h, h+k, l), (-h-k, h, l), (-k, -h, l)),
range(162, 164):
lambda h, k, l: ((h, k, l), (h+k, -h, -l), (k, -h-k, l),
(-k, -h, -l), (k, h, l), (-h, h+k, -l), (-h, -k, -l),
(-k, h+k, -l), (-h-k, k, l), (-h-k, h, l),
(h+k, -k, -l), (h, -h-k, l)),
range(164, 168):
lambda h, k, l: ((h, k, l), (h+k, -h, -l), (k, -h-k, l),
(-h-k, k, -l), (h, -h-k, -l), (h+k, -k, l),
(k, h, -l), (-h, -k, -l), (-k, h+k, -l),
(-h, h+k, l), (-h-k, h, l), (-k, -h, l)),
range(168, 174):
lambda h, k, l: ((h, k, l), (k, -h-k, l), (-k, h+k, l),
(-h, -k, l), (-h-k, h, l), (h+k, -h, l)),
range(174, 175):
lambda h, k, l: ((h, k, l), (-h-k, h, -l), (k, -h-k, l),
(k, -h-k, -l), (-h-k, h, l), (h, k, -l)),
range(175, 177):
lambda h, k, l: ((h, k, l), (h+k, -h, -l), (k, -h-k, l),
(-h-k, h, -l), (h, k, -l), (-k, h+k, l),
(-h, -k, l), (-h, -k, -l), (-k, h+k, -l),
(k, -h-k, -l), (-h-k, h, l), (h+k, -h, l)),
range(177, 183):
lambda h, k, l: ((h, k, l), (k, -h-k, l), (-h-k, k, -l), (h, -h-k, -l),
(-k, -h, -l), (k, h, -l), (-k, h+k, l), (-h, -k, l),
(-h, h+k, -l), (-h-k, h, l), (h+k, -k, -l),
(h+k, -h, l)),
range(183, 187):
lambda h, k, l: ((h, k, l), (k, -h-k, l), (h+k, -k, l), (k, h, l),
(-k, h+k, l), (-h, -k, l), (-h, h+k, l), (-h-k, k, l),
(-h-k, h, l), (-k, -h, l), (h, -h-k, l),
(h+k, -h, l)),
range(187, 189):
lambda h, k, l: ((h, k, l), (-h-k, h, -l), (k, -h-k, l), (h+k, -k, l),
(-k, -h, -l), (h+k, -k, -l), (-h, h+k, -l),
(-h, h+k, l), (k, -h-k, -l), (-h-k, h, l),
(-k, -h, l), (h, k, -l)),
range(189, 191):
lambda h, k, l: ((h, k, l), (-h-k, h, -l), (k, -h-k, l),
(-h-k, k, -l), (h, -h-k, -l), (k, h, -l), (k, h, l),
(-h-k, k, l), (k, -h-k, -l), (-h-k, h, l),
(h, -h-k, l), (h, k, -l)),
range(191, 195):
lambda h, k, l: ((h, k, l), (h+k, -h, -l), (k, h, -l), (k, h, l),
(-k, h+k, l), (-h, h+k, -l), (h+k, -k, -l),
(h, -h-k, l), (-h-k, h, -l), (k, -h-k, l),
(-k, -h, -l), (-h, -k, l), (-h, -k, -l), (-k, -h, l),
(-h-k, k, -l), (h, -h-k, -l), (h+k, -k, l),
(-h, h+k, l), (-k, h+k, -l), (-h-k, k, l), (h, k, -l),
(h+k, -h, l), (k, -h-k, -l), (-h-k, h, l)),
range(195, 200):
lambda h, k, l: ((h, k, l), (-l, -h, k), (-h, k, -l), (k, -l, -h),
(l, h, k), (-k, l, -h), (-k, -l, h), (-l, h, -k),
(-h, -k, l), (h, -k, -l), (l, -h, -k), (k, l, h)),
range(200, 207):
lambda h, k, l: ((h, k, l), (k, -l, -h), (-l, -h, -k), (k, l, -h),
(-l, h, k), (-l, h, -k), (l, h, -k), (l, -h, k),
(k, -l, h), (-h, -k, l), (h, -k, -l), (-h, -k, -l),
(h, -k, l), (-h, k, l), (l, -h, -k), (k, l, h),
(l, h, k), (-k, -l, h), (-l, -h, k), (-k, l, -h),
(h, k, -l), (-h, k, -l), (-k, l, h), (-k, -l, -h)),
range(207, 215):
lambda h, k, l: ((h, k, l), (k, -l, -h), (k, -h, l), (-l, -k, -h),
(k, h, -l), (-l, h, -k), (-k, h, l), (-k, -h, -l),
(-l, k, h), (-h, -k, l), (h, -k, -l), (h, l, -k),
(-h, l, k), (-h, -l, -k), (l, -h, -k), (k, l, h),
(l, h, k), (-k, -l, h), (-l, -h, k), (-k, l, -h),
(h, -l, k), (-h, k, -l), (l, -k, h), (l, k, -h)),
range(215, 221):
lambda h, k, l: ((h, k, l), (h, -l, -k), (k, -l, -h), (-l, k, -h),
(-l, h, -k), (k, h, l), (-h, -k, l), (h, -k, -l),
(h, l, k), (-h, l, -k), (l, -h, -k), (-k, -h, l),
(k, l, h), (-l, -k, h), (l, k, h), (l, h, k),
(-k, -l, h), (-k, h, -l), (-l, -h, k), (k, -h, -l),
(-k, l, -h), (l, -k, -h), (-h, k, -l), (-h, -l, k)),
range(221, 231):
lambda h, k, l: ((h, k, l), (h, -l, -k), (k, -l, -h), (-l, k, -h),
(k, -h, l), (-l, -k, -h), (k, h, -l), (-l, -h, -k),
(-l, h, k), (-l, h, -k), (k, l, -h), (k, h, l),
(-k, h, l), (l, h, -k), (k, -l, h), (-k, -h, -l),
(l, -h, k), (-l, k, h), (-h, -k, l), (h, -k, -l),
(h, l, -k), (-h, l, k), (-h, -l, -k), (-h, -k, -l),
(h, -k, l), (-h, k, l), (l, -h, -k), (-k, -h, l),
(k, l, h), (-l, -k, h), (l, h, k), (-k, -l, h),
(-k, h, -l), (l, k, h), (-h, l, -k), (h, l, k),
(-l, -h, k), (k, -h, -l), (-k, l, -h), (l, -k, -h),
(h, -l, k), (h, k, -l), (-h, k, -l), (-h, -l, k),
(l, -k, h), (-k, l, h), (l, k, -h), (-k, -l, -h))
})
eqhkl_custom = RangeDict({
range(3, 6): lambda h, k, l: ((-h, -k, l), (h, k, l)),
range(6, 10): lambda h, k, l: ((h, k, l), (h, k, -l)),
range(10, 16):
lambda h, k, l: ((-h, -k, l), (-h, -k, -l), (h, k, l), (h, k, -l)),
(48, 50, 59, 68, 70): eqhkl_default[range(47, 75)],
(85, 86, 88): eqhkl_default[range(83, 89)],
(125, 126, 129, 130, 133, 134, 137, 138, 141, 142):
eqhkl_default[range(123, 143)],
range(146, 147): lambda h, k, l: ((h, k, l), (k, l, h), (l, h, k)),
range(148, 149):
lambda h, k, l: ((h, k, l), (-l, -h, -k), (l, h, k), (-k, -l, -h),
(-h, -k, -l), (k, l, h)),
range(155, 156):
lambda h, k, l: ((h, k, l), (-l, -k, -h), (l, h, k), (-k, -h, -l),
(-h, -l, -k), (k, l, h)),
range(160, 162):
lambda h, k, l: ((h, k, l), (l, k, h), (l, h, k), (k, h, l),
(h, l, k), (k, l, h)),
range(166, 168):
lambda h, k, l: ((h, k, l), (-l, -k, -h), (l, h, k), (-k, -h, -l),
(-l, -h, -k), (-k, -l, -h), (l, k, h), (k, h, l),
(h, l, k), (-h, -k, -l), (-h, -l, -k), (k, l, h)),
(201, 203): eqhkl_default[range(200, 207)],
(222, 224, 227, 228): eqhkl_default[range(221, 231)]
})
wp = {'1': {'1a': (7, ('(x, y, z)', ), None)},
'2': {'1a': (0, ('(0, 0, 0)', ), None),
'1b': (0, ('(0, 0, 1/2)', ), None),
'1c': (0, ('(0, 1/2, 0)', ), None),
'1d': (0, ('(1/2, 0, 0)', ), None),
'1e': (0, ('(1/2, 1/2, 0)', ), None),
'1f': (0, ('(1/2, 0, 1/2)', ), None),
'1g': (0, ('(0, 1/2, 1/2)', ), None),
'1h': (0, ('(1/2, 1/2, 1/2)', ), None),
'2i': (7, ('(x, y, z)', '(-x, -y, -z)'), None)},
'3:b': {'1a': (2, ('(0, y, 0)', ), None),
'1b': (2, ('(0, y, 1/2)', ), None),
'1c': (2, ('(1/2, y, 0)', ), None),
'1d': (2, ('(1/2, y, 1/2)', ), None),
'2e': (7, ('(x, y, z)', '(-x, y, -z)'), None)},
'3:c': {'1a': (4, ('(0, 0, z)', ), 'n/a'),
'1b': (4, ('(1/2, 0, z)', ), 'n/a'),
'1c': (4, ('(0, 1/2, z)', ), 'n/a'),
'1d': (4, ('(1/2, 1/2, z)', ), 'n/a'),
'2e': (7, ('(x, y, z)', '(-x, -y, z)'), 'n/a')},
'4:b': {'2a': (7, ('(x, y, z)', '(-x, y+1/2, -z)'), '0k0: k=2n')},
'4:c': {'2a': (7, ('(x, y, z)', '(-x, -y, z+1/2)'), 'n/a')},
'5:b': {'2a': (2, ('(0, y, 0)', '(1/2, y+1/2, 0)'), None),
'2b': (2, ('(0, y, 1/2)', '(1/2, y+1/2, 1/2)'), None),
'4c': (7, ('(x, y, z)', '(x+1/2, y+1/2, z)', '(-x, y, -z)',
'(-x+1/2, y+1/2, -z)'),
'hkl: h+k=2n, h0l: h=2n, 0kl: k=2n, hk0: h+k=2n, '
'0k0: k=2n, h00: h=2n')},
'5:c': {'2a': (4, ('(0, 0, z)', '(0, 1/2, z+1/2)'), 'n/a'),
'2b': (4, ('(1/2, 0, z)', '(1/2, 1/2, z+1/2)'), 'n/a'),
'4c': (7, ('(x, y, z)', '(x, y+1/2, z+1/2)', '(-x, -y, z)',
'(-x, -y+1/2, z+1/2)'), 'n/a')},
'6:b': {'1a': (5, ('(x, 0, z)', ), None),
'1b': (5, ('(x, 1/2, z)', ), None),
'2c': (7, ('(x, y, z)', '(x, -y, z)'), None)},
'6:c': {'1a': (3, ('(x, y, 0)', ), 'n/a'),
'1b': (3, ('(x, y, 1/2)', ), 'n/a'),
'2c': (7, ('(x, y, z)', '(x, y, -z)'), 'n/a')},
'7:b': {'2a': (7, ('(x, y, z)', '(x, -y, z+1/2)'), 'h0l: l=2n, '
'00l: l=2n')},
'7:c': {'2a': (7, ('(x, y, z)', '(x+1/2, y, -z)'), 'n/a')},
'8:b': {'2a': (5, ('(x, 0, z)', '(x+1/2, 1/2, z)'), None),
'4b': (7, ('(x, y, z)', '(x+1/2, y+1/2, z)', '(x, -y, z)',
'(x+1/2, -y+1/2, z)'),
'hkl: h+k=2n, h0l: h=2n, 0kl: k=2n, hk0: h+k=2n, '
'0k0: k=2n, h00: h=2n')},
'8:c': {'2a': (3, ('(x, y, 0)', '(x, y+1/2, 1/2)'), 'n/a'),
'4b': (7, ('(x, y, z)', '(x, y+1/2, z+1/2)', '(x, y, -z)',
'(x, y+1/2, -z+1/2)'), 'n/a')},
'9:b': {'4a': (7, ('(x, y, z)', '(x+1/2, y+1/2, z)', '(x, -y, z+1/2)',
'(x+1/2, -y+1/2, z+1/2)'),
'hkl: h+k=2n, h0l: h,l=2n, 0kl: k=2n, hk0: h+k=2n, '
'0k0: k=2n, h00: h=2n, 00l: l=2n')},
'9:c': {'4a': (7, ('(x, y, z)', '(x, y+1/2, z+1/2)', '(x+1/2, y, -z)',
'(x+1/2, y+1/2, -z+1/2)'), 'n/a')},
'10:b': {'1a': (0, ('(0, 0, 0)', ), None),
'1b': (0, ('(0, 1/2, 0)', ), None),
'1c': (0, ('(0, 0, 1/2)', ), None),
'1d': (0, ('(1/2, 0, 0)', ), None),
'1e': (0, ('(1/2, 1/2, 0)', ), None),
'1f': (0, ('(0, 1/2, 1/2)', ), None),
'1g': (0, ('(1/2, 0, 1/2)', ), None),
'1h': (0, ('(1/2, 1/2, 1/2)', ), None),
'2i': (2, ('(0, y, 0)', '(0, -y, 0)'), None),
'2j': (2, ('(1/2, y, 0)', '(1/2, -y, 0)'), None),
'2k': (2, ('(0, y, 1/2)', '(0, -y, 1/2)'), None),
'2l': (2, ('(1/2, y, 1/2)', '(1/2, -y, 1/2)'), None),
'2m': (5, ('(x, 0, z)', '(-x, 0, -z)'), None),
'2n': (5, ('(x, 1/2, z)', '(-x, 1/2, -z)'), None),
'4o': (7, ('(x, y, z)', '(-x, y, -z)', '(-x, -y, -z)',
'(x, -y, z)'), None)},
'10:c': {'1a': (0, ('(0, 0, 0)', ), 'n/a'),
'1b': (0, ('(0, 0, 1/2)', ), 'n/a'),
'1c': (0, ('(1/2, 0, 0)', ), 'n/a'),
'1d': (0, ('(0, 1/2, 0)', ), 'n/a'),
'1e': (0, ('(0, 1/2, 1/2)', ), 'n/a'),
'1f': (0, ('(1/2, 0, 1/2)', ), 'n/a'),
'1g': (0, ('(1/2, 1/2, 0)', ), 'n/a'),
'1h': (0, ('(1/2, 1/2, 1/2)', ), 'n/a'),
'2i': (4, ('(0, 0, z)', '(0, 0, -z)'), 'n/a'),
'2j': (4, ('(0, 1/2, z)', '(0, 1/2, -z)'), 'n/a'),
'2k': (4, ('(1/2, 0, z)', '(1/2, 0, -z)'), 'n/a'),
'2l': (4, ('(1/2, 1/2, z)', '(1/2, 1/2, -z)'), 'n/a'),
'2m': (3, ('(x, y, 0)', '(-x, -y, 0)'), 'n/a'),
'2n': (3, ('(x, y, 1/2)', '(-x, -y, 1/2)'), 'n/a'),
'4o': (7, ('(x, y, z)', '(-x, -y, z)', '(-x, -y, -z)',
'(x, y, -z)'), 'n/a')},
'11:b': {'2a': (0, ('(0, 0, 0)', '(0, 1/2, 0)'), 'hkl: k=2n'),
'2b': (0, ('(1/2, 0, 0)', '(1/2, 1/2, 0)'), 'hkl: k=2n'),
'2c': (0, ('(0, 0, 1/2)', '(0, 1/2, 1/2)'), 'hkl: k=2n'),
'2d': (0, ('(1/2, 0, 1/2)', '(1/2, 1/2, 1/2)'), 'hkl: k=2n'),
'2e': (5, ('(x, 1/4, z)', '(-x, 3/4, -z)'), None),
'4f': (7, ('(x, y, z)', '(-x, y+1/2, -z)', '(-x, -y, -z)',
'(x, -y+1/2, z)'), '0k0: k=2n')},
'11:c': {'2a': (0, ('(0, 0, 0)', '(0, 0, 1/2)'), 'n/a'),
'2b': (0, ('(0, 1/2, 0)', '(0, 1/2, 1/2)'), 'n/a'),
'2c': (0, ('(1/2, 0, 0)', '(1/2, 0, 1/2)'), 'n/a'),
'2d': (0, ('(1/2, 1/2, 0)', '(1/2, 1/2, 1/2)'), 'n/a'),
'2e': (3, ('(x, y, 1/4)', '(-x, -y, 3/4)'), 'n/a'),
'4f': (7, ('(x, y, z)', '(-x, -y, z+1/2)', '(-x, -y, -z)',
'(x, y, -z+1/2)'), 'n/a')},
'12:b': {'2a': (0, ('(0, 0, 0)', '(1/2, 1/2, 0)'), None),
'2b': (0, ('(0, 1/2, 0)', '(1/2, 0, 0)'), None),
'2c': (0, ('(0, 0, 1/2)', '(1/2, 1/2, 1/2)'), None),
'2d': (0, ('(0, 1/2, 1/2)', '(1/2, 0, 1/2)'), None),
'4e': (0, ('(1/4, 1/4, 0)', '(3/4, 3/4, 0)', '(3/4, 1/4, 0)',
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'4h': (2, ('(0, y, 1/2)', '(1/2, y+1/2, 1/2)', '(0, -y, 1/2)',
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'(-x+1/2, -y+1/2, -z)', '(x, -y, z)',
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'hkl: h+k=2n, h0l: h=2n, 0kl: k=2n, hk0: h+k=2n, '
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'2e': (2, ('(0, y, 1/4)', '(0, -y, 3/4)'), None),
'2f': (2, ('(1/2, y, 1/4)', '(1/2, -y, 3/4)'), None),
'4g': (7, ('(x, y, z)', '(-x, y, -z+1/2)', '(-x, -y, -z)',
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'4g': (7, ('(x, y, z)', '(-x+1/2, -y, z)', '(-x, -y, -z)',
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'4e': (7, ('(x, y, z)', '(-x, y+1/2, -z+1/2)', '(-x, -y, -z)',
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'hkl: h+k=2n, 0kl: k=2n, h0l: h=2n, hk0: h+k=2n, '
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'(x+1/2, -y, -z+1/2)', '(x+1/2, -y+1/2, -z)'),
'hkl: h+k,h+l,k+l=2n, 0kl: k,l=2n, h0l: h,l=2n, '
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'1d': (4, ('(1/2, 1/2, z)', ), None),
'2e': (5, ('(x, 0, z)', '(-x, 0, z)'), None),
'2f': (5, ('(x, 1/2, z)', '(-x, 1/2, z)'), None),
'2g': (6, ('(0, y, z)', '(0, -y, z)'), None),
'2h': (6, ('(1/2, y, z)', '(1/2, -y, z)'), None),
'4i': (7, ('(x, y, z)', '(-x, -y, z)', '(x, -y, z)',
'(-x, y, z)'), None)},
'26': {'2a': (6, ('(0, y, z)', '(0, -y, z+1/2)'), None),
'2b': (6, ('(1/2, y, z)', '(1/2, -y, z+1/2)'), None),
'4c': (7, ('(x, y, z)', '(-x, -y, z+1/2)', '(x, -y, z+1/2)',
'(-x, y, z)'), 'h0l: l=2n, 00l: l=2n')},
'27': {'2a': (4, ('(0, 0, z)', '(0, 0, z+1/2)'), 'hkl: l=2n'),
'2b': (4, ('(0, 1/2, z)', '(0, 1/2, z+1/2)'), 'hkl: l=2n'),
'2c': (4, ('(1/2, 0, z)', '(1/2, 0, z+1/2)'), 'hkl: l=2n'),
'2d': (4, ('(1/2, 1/2, z)', '(1/2, 1/2, z+1/2)'), 'hkl: l=2n'),
'4e': (7, ('(x, y, z)', '(-x, -y, z)', '(x, -y, z+1/2)',
'(-x, y, z+1/2)'), '0kl: l=2n, h0l: l=2n, 00l: l=2n'
)},
'28': {'2a': (4, ('(0, 0, z)', '(1/2, 0, z)'), 'hkl: h=2n'),
'2b': (4, ('(0, 1/2, z)', '(1/2, 1/2, z)'), 'hkl: h=2n'),
'2c': (6, ('(1/4, y, z)', '(3/4, -y, z)'), None),
'4d': (7, ('(x, y, z)', '(-x, -y, z)', '(x+1/2, -y, z)',
'(-x+1/2, y, z)'), 'h0l: h=2n, h00: h=2n')},
'29': {'4a': (7, ('(x, y, z)', '(-x, -y, z+1/2)', '(x+1/2, -y, z)',
'(-x+1/2, y, z+1/2)'),
'0kl: l=2n, h0l: h=2n, h00: h=2n, 00l: l=2n')},
'30': {'2a': (4, ('(0, 0, z)', '(0, 1/2, z+1/2)'), 'hkl: k+l=2n'),
'2b': (4, ('(1/2, 0, z)', '(1/2, 1/2, z+1/2)'), 'hkl: k+l=2n'),
'4c': (7, ('(x, y, z)', '(-x, -y, z)', '(x, -y+1/2, z+1/2)',
'(-x, y+1/2, z+1/2)'),
'0kl: k+l=2n, h0l: l=2n, 0k0: k=2n, 00l: l=2n')},
'31': {'2a': (6, ('(0, y, z)', '(1/2, -y, z+1/2)'), None),
'4b': (7, ('(x, y, z)', '(-x+1/2, -y, z+1/2)',
'(x+1/2, -y, z+1/2)', '(-x, y, z)'),
'h0l: h+l=2n, h00: h=2n, 00l: l=2n')},
'32': {'2a': (4, ('(0, 0, z)', '(1/2, 1/2, z)'), 'hkl: h+k=2n'),
'2b': (4, ('(0, 1/2, z)', '(1/2, 0, z)'), 'hkl: h+k=2n'),
'4c': (7, ('(x, y, z)', '(-x, -y, z)', '(x+1/2, -y+1/2, z)',
'(-x+1/2, y+1/2, z)'),
'0kl: k=2n, h0l: h=2n, h00: h=2n, 0k0: k=2n')},
'33': {'4a': (7, ('(x, y, z)', '(-x, -y, z+1/2)', '(x+1/2, -y+1/2, z)',
'(-x+1/2, y+1/2, z+1/2)'),
'0kl: k+l=2n, h0l: h=2n, h00: h=2n, 0k0: k=2n, 00l: l=2n'
)},
'34': {'2a': (4, ('(0, 0, z)', '(1/2, 1/2, z+1/2)'), 'hkl: h+k+l=2n'),
'2b': (4, ('(0, 1/2, z)', '(1/2, 0, z+1/2)'), 'hkl: h+k+l=2n'),
'4c': (7, ('(x, y, z)', '(-x, -y, z)', '(x+1/2, -y+1/2, z+1/2)',
'(-x+1/2, y+1/2, z+1/2)'),
'0kl: k+l=2n, h0l: h+l=2n, h00: h=2n, 0k0: k=2n, '
'00l: l=2n')},
'35': {'2a': (4, ('(0, 0, z)', '(1/2, 1/2, z)'), None),
'2b': (4, ('(0, 1/2, z)', '(1/2, 0, z)'), None),
'4c': (4, ('(1/4, 1/4, z)', '(3/4, 3/4, z)', '(1/4, 3/4, z)',
'(3/4, 1/4, z)'), 'hkl: h=2n'),
'4d': (5, ('(x, 0, z)', '(x+1/2, 1/2, z)', '(-x, 0, z)',
'(-x+1/2, 1/2, z)'), None),
'4e': (6, ('(0, y, z)', '(1/2, y+1/2, z)', '(0, -y, z)',
'(1/2, -y+1/2, z)'), None),
'8f': (7, ('(x, y, z)', '(x+1/2, y+1/2, z)', '(-x, -y, z)',
'(-x+1/2, -y+1/2, z)', '(x, -y, z)',
'(x+1/2, -y+1/2, z)', '(-x, y, z)',
'(-x+1/2, y+1/2, z)'),
'hkl: h+k=2n, 0kl: k=2n, h0l: h=2n, hk0: h+k=2n, '
'h00: h=2n, 0k0: k=2n')},
'36': {'4a': (6, ('(0, y, z)', '(1/2, y+1/2, z)', '(0, -y, z+1/2)',
'(1/2, -y+1/2, z+1/2)'), None),
'8b': (7, ('(x, y, z)', '(x+1/2, y+1/2, z)', '(-x, -y, z+1/2)',
'(-x+1/2, -y+1/2, z+1/2)', '(x, -y, z+1/2)',
'(x+1/2, -y+1/2, z+1/2)', '(-x, y, z)',
'(-x+1/2, y+1/2, z)'),
'hkl: h+k=2n, 0kl: k=2n, h0l: h,l=2n, hk0: h+k=2n, '
'h00: h=2n, 0k0: k=2n, 00l: l=2n')},
'37': {'4a': (4, ('(0, 0, z)', '(1/2, 1/2, z)', '(0, 0, z+1/2)',
'(1/2, 1/2, z+1/2)'), 'hkl: l=2n'),
'4b': (4, ('(0, 1/2, z)', '(1/2, 0, z)', '(0, 1/2, z+1/2)',
'(1/2, 0, z+1/2)'), 'hkl: l=2n'),
'4c': (4, ('(1/4, 1/4, z)', '(3/4, 3/4, z)', '(1/4, 3/4, z+1/2)',
'(3/4, 1/4, z+1/2)'), 'hkl: k+l=2n'),
'8d': (7, ('(x, y, z)', '(x+1/2, y+1/2, z)', '(-x, -y, z)',
'(-x+1/2, -y+1/2, z)', '(x, -y, z+1/2)',
'(x+1/2, -y+1/2, z+1/2)', '(-x, y, z+1/2)',
'(-x+1/2, y+1/2, z+1/2)'),
'hkl: h+k=2n, 0kl: k,l=2n, h0l: h,l=2n, hk0: h+k=2n, '
'h00: h=2n, 0k0: k=2n, 00l: l=2n')},
'38': {'2a': (4, ('(0, 0, z)', '(0, 1/2, z+1/2)'), None),
'2b': (4, ('(1/2, 0, z)', '(1/2, 1/2, z+1/2)'), None),
'4c': (5, ('(x, 0, z)', '(x, 1/2, z+1/2)', '(-x, 0, z)',
'(-x, 1/2, z+1/2)'), None),
'4d': (6, ('(0, y, z)', '(0, y+1/2, z+1/2)', '(0, -y, z)',
'(0, -y+1/2, z+1/2)'), None),
'4e': (6, ('(1/2, y, z)', '(1/2, y+1/2, z+1/2)', '(1/2, -y, z)',
'(1/2, -y+1/2, z+1/2)'), None),
'8f': (7, ('(x, y, z)', '(x, y+1/2, z+1/2)', '(-x, -y, z)',
'(-x, -y+1/2, z+1/2)', '(x, -y, z)',
'(x, -y+1/2, z+1/2)', '(-x, y, z)',
'(-x, y+1/2, z+1/2)'),
'hkl: k+l=2n, 0kl: k+l=2n, h0l: l=2n, hk0: k=2n, '
'0k0: k=2n, 00l: l=2n')},
'39': {'4a': (4, ('(0, 0, z)', '(0, 1/2, z+1/2)', '(0, 1/2, z)',
'(0, 0, z+1/2)'), 'hkl: k=2n'),
'4b': (4, ('(1/2, 0, z)', '(1/2, 1/2, z+1/2)', '(1/2, 1/2, z)',
'(1/2, 0, z+1/2)'), 'hkl: k=2n'),
'4c': (5, ('(x, 1/4, z)', '(x, 3/4, z+1/2)', '(-x, 3/4, z)',
'(-x, 1/4, z+1/2)'), None),
'8d': (7, ('(x, y, z)', '(x, y+1/2, z+1/2)', '(-x, -y, z)',
'(-x, -y+1/2, z+1/2)', '(x, -y+1/2, z)',
'(x, -y, z+1/2)', '(-x, y+1/2, z)', '(-x, y, z+1/2)'),
'hkl: k+l=2n, 0kl: k,l=2n, h0l: l=2n, hk0: k=2n, '
'0k0: k=2n, 00l: l=2n')},
'40': {'4a': (4, ('(0, 0, z)', '(0, 1/2, z+1/2)', '(1/2, 0, z)',
'(1/2, 1/2, z+1/2)'), 'hkl: h=2n'),
'4b': (6, ('(1/4, y, z)', '(1/4, y+1/2, z+1/2)', '(3/4, -y, z)',
'(3/4, -y+1/2, z+1/2)'), None),
'8c': (7, ('(x, y, z)', '(x, y+1/2, z+1/2)', '(-x, -y, z)',
'(-x, -y+1/2, z+1/2)', '(x+1/2, -y, z)',
'(x+1/2, -y+1/2, z+1/2)', '(-x+1/2, y, z)',
'(-x+1/2, y+1/2, z+1/2)'),
'hkl: k+l=2n, 0kl: k+l=2n, h0l: h,l=2n, hk0: k=2n, '
'h00: h=2n, 0k0: k=2n, 00l: l=2n')},
'41': {'4a': (4, ('(0, 0, z)', '(0, 1/2, z+1/2)', '(1/2, 1/2, z)',
'(1/2, 0, z+1/2)'), 'hkl: h+k=2n'),
'8b': (7, ('(x, y, z)', '(x, y+1/2, z+1/2)', '(-x, -y, z)',
'(-x, -y+1/2, z+1/2)', '(x+1/2, -y+1/2, z)',
'(x+1/2, -y, z+1/2)', '(-x+1/2, y+1/2, z)',
'(-x+1/2, y, z+1/2)'),
'hkl: k+l=2n, 0kl: k,l=2n, h0l: h,l=2n, hk0: k=2n, '
'h00: h=2n, 0k0: k=2n, 00l: l=2n')},
'42': {'4a': (4, ('(0, 0, z)', '(0, 1/2, z+1/2)', '(1/2, 0, z+1/2)',
'(1/2, 1/2, z)'), None),
'8b': (4, ('(1/4, 1/4, z)', '(1/4, 3/4, z+1/2)',
'(3/4, 1/4, z+1/2)', '(3/4, 3/4, z)', '(1/4, 3/4, z)',
'(1/4, 1/4, z+1/2)', '(3/4, 3/4, z+1/2)',
'(3/4, 1/4, z)'), 'hkl: h=2n'),
'8c': (6, ('(0, y, z)', '(0, y+1/2, z+1/2)', '(1/2, y, z+1/2)',
'(1/2, y+1/2, z)', '(0, -y, z)', '(0, -y+1/2, z+1/2)',
'(1/2, -y, z+1/2)', '(1/2, -y+1/2, z)'), None),
'8d': (5, ('(x, 0, z)', '(x, 1/2, z+1/2)', '(x+1/2, 0, z+1/2)',
'(x+1/2, 1/2, z)', '(-x, 0, z)', '(-x, 1/2, z+1/2)',
'(-x+1/2, 0, z+1/2)', '(-x+1/2, 1/2, z)'), None),
'16e': (7, ('(x, y, z)', '(x, y+1/2, z+1/2)',
'(x+1/2, y, z+1/2)', '(x+1/2, y+1/2, z)',
'(-x, -y, z)', '(-x, -y+1/2, z+1/2)',
'(-x+1/2, -y, z+1/2)', '(-x+1/2, -y+1/2, z)',
'(x, -y, z)', '(x, -y+1/2, z+1/2)',
'(x+1/2, -y, z+1/2)', '(x+1/2, -y+1/2, z)',
'(-x, y, z)', '(-x, y+1/2, z+1/2)',
'(-x+1/2, y, z+1/2)', '(-x+1/2, y+1/2, z)'),
'hkl: h+k,h+l,k+l=2n, 0kl: k,l=2n, h0l: h,l=2n, '
'hk0: h,k=2n, h00: h=2n, 0k0: k=2n, 00l: l=2n')},
'43': {'8a': (4, ('(0, 0, z)', '(1/2, 0, z+1/2)', '(0, 1/2, z+1/2)',
'(1/2, 1/2, z)', '(1/4, 1/4, z+1/4)',
'(3/4, 1/4, z+3/4)', '(1/4, 3/4, z+3/4)',
'(3/4, 3/4, z+1/4)'), 'hkl: h=2n+1 or h+k+l=4n'),
'16b': (7, ('(x, y, z)', '(x+1/2, y, z+1/2)',
'(x, y+1/2, z+1/2)', '(x+1/2, y+1/2, z)',
'(-x, -y, z)', '(-x+1/2, -y, z+1/2)',
'(-x, -y+1/2, z+1/2)', '(-x+1/2, -y+1/2, z)',
'(x+1/4, -y+1/4, z+1/4)', '(x+3/4, -y+1/4, z+3/4)',
'(x+1/4, -y+3/4, z+3/4)', '(x+3/4, -y+3/4, z+1/4)',
'(-x+1/4, y+1/4, z+1/4)', '(-x+3/4, y+1/4, z+3/4)',
'(-x+1/4, y+3/4, z+3/4)', '(-x+3/4, y+3/4, z+1/4)'),
'hkl: h+k,h+l,k+l=2n, 0kl: k+l=4n, k,l=2n, h0l: h+l=4n, '
'h,l=2n, hk0: h,k=2n, h00: h=4n, 0k0: k=4n, 00l: l=4n')},
'44': {'2a': (4, ('(0, 0, z)', '(1/2, 1/2, z+1/2)'), None),
'2b': (4, ('(0, 1/2, z)', '(1/2, 0, z+1/2)'), None),
'4c': (5, ('(x, 0, z)', '(x+1/2, 1/2, z+1/2)', '(-x, 0, z)',
'(-x+1/2, 1/2, z+1/2)'), None),
'4d': (6, ('(0, y, z)', '(1/2, y+1/2, z+1/2)', '(0, -y, z)',
'(1/2, -y+1/2, z+1/2)'), None),
'8e': (7, ('(x, y, z)', '(x+1/2, y+1/2, z+1/2)', '(-x, -y, z)',
'(-x+1/2, -y+1/2, z+1/2)', '(x, -y, z)',
'(x+1/2, -y+1/2, z+1/2)', '(-x, y, z)',
'(-x+1/2, y+1/2, z+1/2)'),
'hkl: h+k+l=2n, 0kl: k+l=2n, h0l: h+l=2n, hk0: h+k=2n, '
'h00: h=2n, 0k0: k=2n, 00l: l=2n')},
'45': {'4a': (4, ('(0, 0, z)', '(1/2, 1/2, z+1/2)', '(1/2, 1/2, z)',
'(0, 0, z+1/2)'), 'hkl: l=2n'),
'4b': (4, ('(0, 1/2, z)', '(1/2, 0, z+1/2)', '(1/2, 0, z)',
'(0, 1/2, z+1/2)'), 'hkl: l=2n'),
'8c': (7, ('(x, y, z)', '(x+1/2, y+1/2, z+1/2)', '(-x, -y, z)',
'(-x+1/2, -y+1/2, z+1/2)', '(x+1/2, -y+1/2, z)',
'(x, -y, z+1/2)', '(-x+1/2, y+1/2, z)',
'(-x, y, z+1/2)'),
'hkl: h+k+l=2n, 0kl: k,l=2n, h0l: h,l=2n, hk0: h+k=2n, '
'h00: h=2n, 0k0: k=2n, 00l: l=2n')},
'46': {'4a': (4, ('(0, 0, z)', '(1/2, 1/2, z+1/2)', '(1/2, 0, z)',
'(0, 1/2, z+1/2)'), 'hkl: h=2n'),
'4b': (6, ('(1/4, y, z)', '(3/4, y+1/2, z+1/2)', '(3/4, -y, z)',
'(1/4, -y+1/2, z+1/2)'), None),
'8c': (7, ('(x, y, z)', '(x+1/2, y+1/2, z+1/2)', '(-x, -y, z)',
'(-x+1/2, -y+1/2, z+1/2)', '(x+1/2, -y, z)',
'(x, -y+1/2, z+1/2)', '(-x+1/2, y, z)',
'(-x, y+1/2, z+1/2)'),
'hkl: h+k+l=2n, 0kl: k+l=2n, h0l: h,l=2n, hk0: h+k=2n, '
'h00: h=2n, 0k0: k=2n, 00l: l=2n')},
'47': {'8A': (7, ('(x, y, z)', '(-x, -y, z)', '(-x, y, -z)',
'(x, -y, -z)', '(-x, -y, -z)', '(x, y, -z)',
'(x, -y, z)', '(-x, y, z)'), None),
'1a': (0, ('(0, 0, 0)', ), None),
'1b': (0, ('(1/2, 0, 0)', ), None),
'1c': (0, ('(0, 0, 1/2)', ), None),
'1d': (0, ('(1/2, 0, 1/2)', ), None),
'1e': (0, ('(0, 1/2, 0)', ), None),
'1f': (0, ('(1/2, 1/2, 0)', ), None),
'1g': (0, ('(0, 1/2, 1/2)', ), None),
'1h': (0, ('(1/2, 1/2, 1/2)', ), None),
'2i': (1, ('(x, 0, 0)', '(-x, 0, 0)'), None),
'2j': (1, ('(x, 0, 1/2)', '(-x, 0, 1/2)'), None),
'2k': (1, ('(x, 1/2, 0)', '(-x, 1/2, 0)'), None),
'2l': (1, ('(x, 1/2, 1/2)', '(-x, 1/2, 1/2)'), None),
'2m': (2, ('(0, y, 0)', '(0, -y, 0)'), None),
'2n': (2, ('(0, y, 1/2)', '(0, -y, 1/2)'), None),
'2o': (2, ('(1/2, y, 0)', '(1/2, -y, 0)'), None),
'2p': (2, ('(1/2, y, 1/2)', '(1/2, -y, 1/2)'), None),
'2q': (4, ('(0, 0, z)', '(0, 0, -z)'), None),
'2r': (4, ('(0, 1/2, z)', '(0, 1/2, -z)'), None),
'2s': (4, ('(1/2, 0, z)', '(1/2, 0, -z)'), None),
'2t': (4, ('(1/2, 1/2, z)', '(1/2, 1/2, -z)'), None),
'4u': (6, ('(0, y, z)', '(0, -y, z)', '(0, y, -z)',
'(0, -y, -z)'), None),
'4v': (6, ('(1/2, y, z)', '(1/2, -y, z)', '(1/2, y, -z)',
'(1/2, -y, -z)'), None),
'4w': (5, ('(x, 0, z)', '(-x, 0, z)', '(-x, 0, -z)',
'(x, 0, -z)'), None),
'4x': (5, ('(x, 1/2, z)', '(-x, 1/2, z)', '(-x, 1/2, -z)',
'(x, 1/2, -z)'), None),
'4y': (3, ('(x, y, 0)', '(-x, -y, 0)', '(-x, y, 0)',
'(x, -y, 0)'), None),
'4z': (3, ('(x, y, 1/2)', '(-x, -y, 1/2)', '(-x, y, 1/2)',
'(x, -y, 1/2)'), None)},
'48:1': {'2a': (0, ('(0, 0, 0)', '(1/2, 1/2, 1/2)'), 'hkl: h+k+l=2n'),
'2b': (0, ('(1/2, 0, 0)', '(0, 1/2, 1/2)'), 'hkl: h+k+l=2n'),
'2c': (0, ('(0, 0, 1/2)', '(1/2, 1/2, 0)'), 'hkl: h+k+l=2n'),
'2d': (0, ('(0, 1/2, 0)', '(1/2, 0, 1/2)'), 'hkl: h+k+l=2n'),
'4e': (0, ('(1/4, 1/4, 1/4)', '(3/4, 3/4, 1/4)',
'(3/4, 1/4, 3/4)', '(1/4, 3/4, 3/4)'),
'hkl: h+k,h+l,k+l=2n'),
'4f': (0, ('(3/4, 3/4, 3/4)', '(1/4, 1/4, 3/4)',
'(1/4, 3/4, 1/4)', '(3/4, 1/4, 1/4)'),
'hkl: h+k,h+l,k+l=2n'),
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'(1/2, 1/2, z)', '(0, 0, -z)', '(0, 1/2, -z+1/2)',
'(1/2, 0, -z+1/2)', '(1/2, 1/2, -z)',
'(1/4, 1/4, -z+1/4)', '(1/4, 3/4, -z+3/4)',
'(3/4, 1/4, -z+3/4)', '(3/4, 3/4, -z+1/4)',
'(1/4, 1/4, z+1/4)', '(1/4, 3/4, z+3/4)',
'(3/4, 1/4, z+3/4)', '(3/4, 3/4, z+1/4)'),
'hkl: h=2n+1 or h+k+l=4n'),
'32h': (7, ('(x, y, z)', '(x, y+1/2, z+1/2)',
'(x+1/2, y, z+1/2)', '(x+1/2, y+1/2, z)',
'(-x, -y, z)', '(-x, -y+1/2, z+1/2)',
'(-x+1/2, -y, z+1/2)', '(-x+1/2, -y+1/2, z)',
'(-x, y, -z)', '(-x, y+1/2, -z+1/2)',
'(-x+1/2, y, -z+1/2)', '(-x+1/2, y+1/2, -z)',
'(x, -y, -z)', '(x, -y+1/2, -z+1/2)',
'(x+1/2, -y, -z+1/2)', '(x+1/2, -y+1/2, -z)',
'(-x+1/4, -y+1/4, -z+1/4)',
'(-x+1/4, -y+3/4, -z+3/4)',
'(-x+3/4, -y+1/4, -z+3/4)',
'(-x+3/4, -y+3/4, -z+1/4)',
'(x+1/4, y+1/4, -z+1/4)', '(x+1/4, y+3/4, -z+3/4)',
'(x+3/4, y+1/4, -z+3/4)', '(x+3/4, y+3/4, -z+1/4)',
'(x+1/4, -y+1/4, z+1/4)', '(x+1/4, -y+3/4, z+3/4)',
'(x+3/4, -y+1/4, z+3/4)', '(x+3/4, -y+3/4, z+1/4)',
'(-x+1/4, y+1/4, z+1/4)', '(-x+1/4, y+3/4, z+3/4)',
'(-x+3/4, y+1/4, z+3/4)', '(-x+3/4, y+3/4, z+1/4)'
),
'hkl: h+k,h+l,k+l=2n, 0kl: k+l=4n, k,l=2n, '
'h0l: h+l=4n, h,l=2n, hk0: h+k=4n, h,k=2n, h00: h=4n, '
'0k0: k=4n, 00l: l=4n')},
'70:2': {'8a': (0, ('(1/8, 1/8, 1/8)', '(1/8, 5/8, 5/8)',
'(5/8, 1/8, 5/8)', '(5/8, 5/8, 1/8)',
'(7/8, 7/8, 7/8)', '(7/8, 3/8, 3/8)',
'(3/8, 7/8, 3/8)', '(3/8, 3/8, 7/8)'), 'n/a'),
'8b': (0, ('(1/8, 1/8, 5/8)', '(1/8, 5/8, 1/8)',
'(5/8, 1/8, 1/8)', '(5/8, 5/8, 5/8)',
'(7/8, 7/8, 3/8)', '(7/8, 3/8, 7/8)',
'(3/8, 7/8, 7/8)', '(3/8, 3/8, 3/8)'), 'n/a'),
'16c': (0, ('(0, 0, 0)', '(0, 1/2, 1/2)', '(1/2, 0, 1/2)',
'(1/2, 1/2, 0)', '(3/4, 3/4, 0)',
'(3/4, 1/4, 1/2)', '(1/4, 3/4, 1/2)',
'(1/4, 1/4, 0)', '(3/4, 0, 3/4)',
'(3/4, 1/2, 1/4)', '(1/4, 0, 1/4)',
'(1/4, 1/2, 3/4)', '(0, 3/4, 3/4)',
'(0, 1/4, 1/4)', '(1/2, 3/4, 1/4)',
'(1/2, 1/4, 3/4)'), 'n/a'),
'16d': (0, ('(1/2, 1/2, 1/2)', '(1/2, 0, 0)', '(0, 1/2, 0)',
'(0, 0, 1/2)', '(1/4, 1/4, 1/2)', '(1/4, 3/4, 0)',
'(3/4, 1/4, 0)', '(3/4, 3/4, 1/2)',
'(1/4, 1/2, 1/4)', '(1/4, 0, 3/4)',
'(3/4, 1/2, 3/4)', '(3/4, 0, 1/4)',
'(1/2, 1/4, 1/4)', '(1/2, 3/4, 3/4)',
'(0, 1/4, 3/4)', '(0, 3/4, 1/4)'), 'n/a'),
'16e': (1, ('(x, 1/8, 1/8)', '(x, 5/8, 5/8)',
'(x+1/2, 1/8, 5/8)', '(x+1/2, 5/8, 1/8)',
'(-x+3/4, 5/8, 1/8)', '(-x+3/4, 1/8, 5/8)',
'(-x+1/4, 5/8, 5/8)', '(-x+1/4, 1/8, 1/8)',
'(-x, 7/8, 7/8)', '(-x, 3/8, 3/8)',
'(-x+1/2, 7/8, 3/8)', '(-x+1/2, 3/8, 7/8)',
'(x+1/4, 3/8, 7/8)', '(x+1/4, 7/8, 3/8)',
'(x+3/4, 3/8, 3/8)', '(x+3/4, 7/8, 7/8)'), 'n/a'),
'16f': (2, ('(1/8, y, 1/8)', '(1/8, y+1/2, 5/8)',
'(5/8, y, 5/8)', '(5/8, y+1/2, 1/8)',
'(5/8, -y+3/4, 1/8)', '(5/8, -y+1/4, 5/8)',
'(1/8, -y+3/4, 5/8)', '(1/8, -y+1/4, 1/8)',
'(7/8, -y, 7/8)', '(7/8, -y+1/2, 3/8)',
'(3/8, -y, 3/8)', '(3/8, -y+1/2, 7/8)',
'(3/8, y+1/4, 7/8)', '(3/8, y+3/4, 3/8)',
'(7/8, y+1/4, 3/8)', '(7/8, y+3/4, 7/8)'), 'n/a'),
'16g': (4, ('(1/8, 1/8, z)', '(1/8, 5/8, z+1/2)',
'(5/8, 1/8, z+1/2)', '(5/8, 5/8, z)',
'(5/8, 1/8, -z+3/4)', '(5/8, 5/8, -z+1/4)',
'(1/8, 1/8, -z+1/4)', '(1/8, 5/8, -z+3/4)',
'(7/8, 7/8, -z)', '(7/8, 3/8, -z+1/2)',
'(3/8, 7/8, -z+1/2)', '(3/8, 3/8, -z)',
'(3/8, 7/8, z+1/4)', '(3/8, 3/8, z+3/4)',
'(7/8, 7/8, z+3/4)', '(7/8, 3/8, z+1/4)'), 'n/a'),
'32h': (7, ('(x, y, z)', '(x, y+1/2, z+1/2)',
'(x+1/2, y, z+1/2)', '(x+1/2, y+1/2, z)',
'(-x+3/4, -y+3/4, z)', '(-x+3/4, -y+1/4, z+1/2)',
'(-x+1/4, -y+3/4, z+1/2)', '(-x+1/4, -y+1/4, z)',
'(-x+3/4, y, -z+3/4)', '(-x+3/4, y+1/2, -z+1/4)',
'(-x+1/4, y, -z+1/4)', '(-x+1/4, y+1/2, -z+3/4)',
'(x, -y+3/4, -z+3/4)', '(x, -y+1/4, -z+1/4)',
'(x+1/2, -y+3/4, -z+1/4)',
'(x+1/2, -y+1/4, -z+3/4)', '(-x, -y, -z)',
'(-x, -y+1/2, -z+1/2)', '(-x+1/2, -y, -z+1/2)',
'(-x+1/2, -y+1/2, -z)', '(x+1/4, y+1/4, -z)',
'(x+1/4, y+3/4, -z+1/2)', '(x+3/4, y+1/4, -z+1/2)',
'(x+3/4, y+3/4, -z)', '(x+1/4, -y, z+1/4)',
'(x+1/4, -y+1/2, z+3/4)', '(x+3/4, -y, z+3/4)',
'(x+3/4, -y+1/2, z+1/4)', '(-x, y+1/4, z+1/4)',
'(-x, y+3/4, z+3/4)', '(-x+1/2, y+1/4, z+3/4)',
'(-x+1/2, y+3/4, z+1/4)'), 'n/a')},
'71': {'2a': (0, ('(0, 0, 0)', '(1/2, 1/2, 1/2)'), None),
'2b': (0, ('(0, 1/2, 1/2)', '(1/2, 0, 0)'), None),
'2c': (0, ('(1/2, 1/2, 0)', '(0, 0, 1/2)'), None),
'2d': (0, ('(1/2, 0, 1/2)', '(0, 1/2, 0)'), None),
'4e': (1, ('(x, 0, 0)', '(x+1/2, 1/2, 1/2)', '(-x, 0, 0)',
'(-x+1/2, 1/2, 1/2)'), None),
'4f': (1, ('(x, 1/2, 0)', '(x+1/2, 0, 1/2)', '(-x, 1/2, 0)',
'(-x+1/2, 0, 1/2)'), None),
'4g': (2, ('(0, y, 0)', '(1/2, y+1/2, 1/2)', '(0, -y, 0)',
'(1/2, -y+1/2, 1/2)'), None),
'4h': (2, ('(0, y, 1/2)', '(1/2, y+1/2, 0)', '(0, -y, 1/2)',
'(1/2, -y+1/2, 0)'), None),
'4i': (4, ('(0, 0, z)', '(1/2, 1/2, z+1/2)', '(0, 0, -z)',
'(1/2, 1/2, -z+1/2)'), None),
'4j': (4, ('(1/2, 0, z)', '(0, 1/2, z+1/2)', '(1/2, 0, -z)',
'(0, 1/2, -z+1/2)'), None),
'8k': (0, ('(1/4, 1/4, 1/4)', '(3/4, 3/4, 3/4)',
'(3/4, 3/4, 1/4)', '(1/4, 1/4, 3/4)',
'(3/4, 1/4, 3/4)', '(1/4, 3/4, 1/4)',
'(1/4, 3/4, 3/4)', '(3/4, 1/4, 1/4)'), 'hkl: k,l=2n'),
'8l': (6, ('(0, y, z)', '(1/2, y+1/2, z+1/2)', '(0, -y, z)',
'(1/2, -y+1/2, z+1/2)', '(0, y, -z)',
'(1/2, y+1/2, -z+1/2)', '(0, -y, -z)',
'(1/2, -y+1/2, -z+1/2)'), None),
'8m': (5, ('(x, 0, z)', '(x+1/2, 1/2, z+1/2)', '(-x, 0, z)',
'(-x+1/2, 1/2, z+1/2)', '(-x, 0, -z)',
'(-x+1/2, 1/2, -z+1/2)', '(x, 0, -z)',
'(x+1/2, 1/2, -z+1/2)'), None),
'8n': (3, ('(x, y, 0)', '(x+1/2, y+1/2, 1/2)', '(-x, -y, 0)',
'(-x+1/2, -y+1/2, 1/2)', '(-x, y, 0)',
'(-x+1/2, y+1/2, 1/2)', '(x, -y, 0)',
'(x+1/2, -y+1/2, 1/2)'), None),
'16o': (7, ('(x, y, z)', '(x+1/2, y+1/2, z+1/2)', '(-x, -y, z)',
'(-x+1/2, -y+1/2, z+1/2)', '(-x, y, -z)',
'(-x+1/2, y+1/2, -z+1/2)', '(x, -y, -z)',
'(x+1/2, -y+1/2, -z+1/2)', '(-x, -y, -z)',
'(-x+1/2, -y+1/2, -z+1/2)', '(x, y, -z)',
'(x+1/2, y+1/2, -z+1/2)', '(x, -y, z)',
'(x+1/2, -y+1/2, z+1/2)', '(-x, y, z)',
'(-x+1/2, y+1/2, z+1/2)'),
'hkl: h+k+l=2n, 0kl: k+l=2n, h0l: h+l=2n, hk0: h+k=2n, '
'h00: h=2n, 0k0: k=2n, 00l: l=2n')},
'72': {'4a': (0, ('(0, 0, 1/4)', '(1/2, 1/2, 3/4)', '(0, 0, 3/4)',
'(1/2, 1/2, 1/4)'), 'hkl: l=2n'),
'4b': (0, ('(1/2, 0, 1/4)', '(0, 1/2, 3/4)', '(1/2, 0, 3/4)',
'(0, 1/2, 1/4)'), 'hkl: l=2n'),
'4c': (0, ('(0, 0, 0)', '(1/2, 1/2, 1/2)', '(1/2, 1/2, 0)',
'(0, 0, 1/2)'), 'hkl: l=2n'),
'4d': (0, ('(1/2, 0, 0)', '(0, 1/2, 1/2)', '(0, 1/2, 0)',
'(1/2, 0, 1/2)'), 'hkl: l=2n'),
'8e': (0, ('(1/4, 1/4, 1/4)', '(3/4, 3/4, 3/4)',
'(3/4, 3/4, 1/4)', '(1/4, 1/4, 3/4)',
'(1/4, 3/4, 3/4)', '(3/4, 1/4, 1/4)',
'(3/4, 1/4, 3/4)', '(1/4, 3/4, 1/4)'), 'hkl: k,l=2n'),
'8f': (1, ('(x, 0, 1/4)', '(x+1/2, 1/2, 3/4)', '(-x, 0, 1/4)',
'(-x+1/2, 1/2, 3/4)', '(-x, 0, 3/4)',
'(-x+1/2, 1/2, 1/4)', '(x, 0, 3/4)',
'(x+1/2, 1/2, 1/4)'), 'hkl: l=2n'),
'8g': (2, ('(0, y, 1/4)', '(1/2, y+1/2, 3/4)', '(0, -y, 1/4)',
'(1/2, -y+1/2, 3/4)', '(0, -y, 3/4)',
'(1/2, -y+1/2, 1/4)', '(0, y, 3/4)',
'(1/2, y+1/2, 1/4)'), 'hkl: l=2n'),
'8h': (4, ('(0, 0, z)', '(1/2, 1/2, z+1/2)', '(1/2, 1/2, -z)',
'(0, 0, -z+1/2)', '(0, 0, -z)', '(1/2, 1/2, -z+1/2)',
'(1/2, 1/2, z)', '(0, 0, z+1/2)'), 'hkl: l=2n'),
'8i': (4, ('(0, 1/2, z)', '(1/2, 0, z+1/2)', '(1/2, 0, -z)',
'(0, 1/2, -z+1/2)', '(0, 1/2, -z)',
'(1/2, 0, -z+1/2)', '(1/2, 0, z)', '(0, 1/2, z+1/2)'),
'hkl: l=2n'),
'8j': (3, ('(x, y, 0)', '(x+1/2, y+1/2, 1/2)', '(-x, -y, 0)',
'(-x+1/2, -y+1/2, 1/2)', '(-x+1/2, y+1/2, 0)',
'(-x, y, 1/2)', '(x+1/2, -y+1/2, 0)', '(x, -y, 1/2)'),
None),
'16k': (7, ('(x, y, z)', '(x+1/2, y+1/2, z+1/2)', '(-x, -y, z)',
'(-x+1/2, -y+1/2, z+1/2)', '(-x+1/2, y+1/2, -z)',
'(-x, y, -z+1/2)', '(x+1/2, -y+1/2, -z)',
'(x, -y, -z+1/2)', '(-x, -y, -z)',
'(-x+1/2, -y+1/2, -z+1/2)', '(x, y, -z)',
'(x+1/2, y+1/2, -z+1/2)', '(x+1/2, -y+1/2, z)',
'(x, -y, z+1/2)', '(-x+1/2, y+1/2, z)',
'(-x, y, z+1/2)'),
'hkl: h+k+l=2n, 0kl: k,l=2n, h0l: h,l=2n, hk0: h+k=2n, '
'h00: h=2n, 0k0: k=2n, 00l: l=2n')},
'73': {'8a': (0, ('(0, 0, 0)', '(1/2, 1/2, 1/2)', '(1/2, 0, 1/2)',
'(0, 1/2, 0)', '(0, 1/2, 1/2)', '(1/2, 0, 0)',
'(1/2, 1/2, 0)', '(0, 0, 1/2)'), 'hkl: k,l=2n'),
'8b': (0, ('(1/4, 1/4, 1/4)', '(3/4, 3/4, 3/4)',
'(1/4, 3/4, 3/4)', '(3/4, 1/4, 1/4)',
'(3/4, 3/4, 1/4)', '(1/4, 1/4, 3/4)',
'(3/4, 1/4, 3/4)', '(1/4, 3/4, 1/4)'), 'hkl: k,l=2n'),
'8c': (1, ('(x, 0, 1/4)', '(x+1/2, 1/2, 3/4)',
'(-x+1/2, 0, 3/4)', '(-x, 1/2, 1/4)', '(-x, 0, 3/4)',
'(-x+1/2, 1/2, 1/4)', '(x+1/2, 0, 1/4)',
'(x, 1/2, 3/4)'), 'hkl: h=2n'),
'8d': (2, ('(1/4, y, 0)', '(3/4, y+1/2, 1/2)', '(1/4, -y, 1/2)',
'(3/4, -y+1/2, 0)', '(3/4, -y, 0)',
'(1/4, -y+1/2, 1/2)', '(3/4, y, 1/2)',
'(1/4, y+1/2, 0)'), 'hkl: k=2n'),
'8e': (4, ('(0, 1/4, z)', '(1/2, 3/4, z+1/2)',
'(0, 3/4, -z+1/2)', '(1/2, 1/4, -z)', '(0, 3/4, -z)',
'(1/2, 1/4, -z+1/2)', '(0, 1/4, z+1/2)',
'(1/2, 3/4, z)'), 'hkl: l=2n'),
'16f': (7, ('(x, y, z)', '(x+1/2, y+1/2, z+1/2)',
'(-x+1/2, -y, z+1/2)', '(-x, -y+1/2, z)',
'(-x, y+1/2, -z+1/2)', '(-x+1/2, y, -z)',
'(x+1/2, -y+1/2, -z)', '(x, -y, -z+1/2)',
'(-x, -y, -z)', '(-x+1/2, -y+1/2, -z+1/2)',
'(x+1/2, y, -z+1/2)', '(x, y+1/2, -z)',
'(x, -y+1/2, z+1/2)', '(x+1/2, -y, z)',
'(-x+1/2, y+1/2, z)', '(-x, y, z+1/2)'),
'hkl: h+k+l=2n, 0kl: k,l=2n, h0l: h,l=2n, hk0: h,k=2n, '
'h00: h=2n, 0k0: k=2n, 00l: l=2n')},
'74': {'4a': (0, ('(0, 0, 0)', '(1/2, 1/2, 1/2)', '(0, 1/2, 0)',
'(1/2, 0, 1/2)'), 'hkl: k=2n'), # wrong in ITA?
'4b': (0, ('(0, 0, 1/2)', '(1/2, 1/2, 0)', '(0, 1/2, 1/2)',
'(1/2, 0, 0)'), 'hkl: k=2n'), # wrong in ITA?
'4c': (0, ('(1/4, 1/4, 1/4)', '(3/4, 3/4, 3/4)',
'(3/4, 1/4, 1/4)', '(1/4, 3/4, 3/4)'), 'hkl: h=2n'),
'4d': (0, ('(1/4, 1/4, 3/4)', '(3/4, 3/4, 1/4)',
'(3/4, 1/4, 3/4)', '(1/4, 3/4, 1/4)'), 'hkl: h=2n'),
'4e': (4, ('(0, 1/4, z)', '(1/2, 3/4, z+1/2)', '(0, 3/4, -z)',
'(1/2, 1/4, -z+1/2)'), None),
'8f': (1, ('(x, 0, 0)', '(x+1/2, 1/2, 1/2)', '(-x, 1/2, 0)',
'(-x+1/2, 0, 1/2)', '(-x, 0, 0)',
'(-x+1/2, 1/2, 1/2)', '(x, 1/2, 0)',
'(x+1/2, 0, 1/2)'), 'hkl: k=2n'),
'8g': (2, ('(1/4, y, 1/4)', '(3/4, y+1/2, 3/4)',
'(3/4, -y+1/2, 1/4)', '(1/4, -y, 3/4)',
'(3/4, -y, 3/4)', '(1/4, -y+1/2, 1/4)',
'(1/4, y+1/2, 3/4)', '(3/4, y, 1/4)'), 'hkl: h=2n'),
'8h': (6, ('(0, y, z)', '(1/2, y+1/2, z+1/2)', '(0, -y+1/2, z)',
'(1/2, -y, z+1/2)', '(0, y+1/2, -z)',
'(1/2, y, -z+1/2)', '(0, -y, -z)',
'(1/2, -y+1/2, -z+1/2)'), None),
'8i': (5, ('(x, 1/4, z)', '(x+1/2, 3/4, z+1/2)', '(-x, 1/4, z)',
'(-x+1/2, 3/4, z+1/2)', '(-x, 3/4, -z)',
'(-x+1/2, 1/4, -z+1/2)', '(x, 3/4, -z)',
'(x+1/2, 1/4, -z+1/2)'), None),
'16j': (7, ('(x, y, z)', '(x+1/2, y+1/2, z+1/2)',
'(-x, -y+1/2, z)', '(-x+1/2, -y, z+1/2)',
'(-x, y+1/2, -z)', '(-x+1/2, y, -z+1/2)',
'(x, -y, -z)', '(x+1/2, -y+1/2, -z+1/2)',
'(-x, -y, -z)', '(-x+1/2, -y+1/2, -z+1/2)',
'(x, y+1/2, -z)', '(x+1/2, y, -z+1/2)',
'(x, -y+1/2, z)', '(x+1/2, -y, z+1/2)', '(-x, y, z)',
'(-x+1/2, y+1/2, z+1/2)'),
'hkl: h+k+l=2n, 0kl: k+l=2n, h0l: h+l=2n, hk0: h,k=2n, '
'h00: h=2n, 0k0: k=2n, 00l: l=2n')},
'75': {'1a': (4, ('(0, 0, z)', ), None),
'1b': (4, ('(1/2, 1/2, z)', ), None),
'2c': (4, ('(0, 1/2, z)', '(1/2, 0, z)'), 'hkl: h+k=2n'),
'4d': (7, ('(x, y, z)', '(-x, -y, z)', '(-y, x, z)',
'(y, -x, z)'), None)},
'76': {'4a': (7, ('(x, y, z)', '(-x, -y, z+1/2)', '(-y, x, z+1/4)',
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'(y, -x, z)', '(-x, y, -z)', '(x, -y, -z)',
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'2c': (4, ('(0, 1/2, z)', '(1/2, 0, -z)'), 'hk0: h+k=2n'),
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'4e': (1, ('(x, x, 0)', '(-x, -x, 0)', '(-x+1/2, x+1/2, 0)',
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'8g': (7, ('(x, y, z)', '(-x, -y, z)', '(-y+1/2, x+1/2, z)',
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'91': {'4a': (2, ('(0, y, 0)', '(0, -y, 1/2)', '(-y, 0, 1/4)',
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'4c': (1, ('(x, x, 3/8)', '(-x, -x, 7/8)', '(-x, x, 5/8)',
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'8d': (7, ('(x, y, z)', '(-x, -y, z+1/2)', '(-y, x, z+1/4)',
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'93': {'2a': (0, ('(0, 0, 0)', '(0, 0, 1/2)'), 'hkl: l=2n'),
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'2d': (0, ('(0, 1/2, 1/2)', '(1/2, 0, 0)'), 'hkl: h+k+l=2n'),
'2e': (0, ('(0, 0, 1/4)', '(0, 0, 3/4)'), 'hkl: l=2n'),
'2f': (0, ('(1/2, 1/2, 1/4)', '(1/2, 1/2, 3/4)'), 'hkl: l=2n'),
'4g': (4, ('(0, 0, z)', '(0, 0, z+1/2)', '(0, 0, -z)',
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'4h': (4, ('(1/2, 1/2, z)', '(1/2, 1/2, z+1/2)',
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'4i': (4, ('(0, 1/2, z)', '(1/2, 0, z+1/2)', '(0, 1/2, -z)',
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'4j': (1, ('(x, 0, 0)', '(-x, 0, 0)', '(0, x, 1/2)',
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'4k': (1, ('(x, 1/2, 1/2)', '(-x, 1/2, 1/2)', '(1/2, x, 0)',
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'(x+1/2, -y+1/2, -z+1/2)', '(y, x, -z)',
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'4c': (1, ('(x, x, 5/8)', '(-x, -x, 1/8)', '(-x, x, 3/8)',
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'4c': (0, ('(0, 1/2, 0)', '(1/2, 0, 1/2)', '(1/2, 0, 0)',
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'(-x+1/2, x+1/2, 1/2)', '(x, -x, 0)',
'(x+1/2, -x+1/2, 1/2)'), None),
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'(x+1/2, -y+1/2, -z+1/2)', '(y, x, -z)',
'(y+1/2, x+1/2, -z+1/2)', '(-y, -x, -z)',
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'hkl: h+k+l=2n, hk0: h+k=2n, 0kl: k+l=2n, hhl: l=2n, '
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'8d': (1, ('(x, x, 0)', '(x+1/2, x+1/2, 1/2)',
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'(x+1/2, -x, 3/4)', '(x, -x+1/2, 1/4)'),
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'8e': (1, ('(-x, x, 0)', '(-x+1/2, x+1/2, 1/2)',
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'8f': (1, ('(x, 1/4, 1/8)', '(x+1/2, 3/4, 5/8)',
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'(-x+1/2, y, -z+3/4)', '(-x, y+1/2, -z+1/4)',
'(x, -y+1/2, -z+1/4)', '(x+1/2, -y, -z+3/4)',
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'(-y, -x, -z)', '(-y+1/2, -x+1/2, -z+1/2)'),
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'2c': (4, ('(1/2, 0, z)', '(0, 1/2, z)'), 'hkl: h+k=2n'),
'4d': (5, ('(x, x, z)', '(-x, -x, z)', '(-x, x, z)',
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'4e': (5, ('(x, 0, z)', '(-x, 0, z)', '(0, x, z)', '(0, -x, z)'),
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'4f': (5, ('(x, 1/2, z)', '(-x, 1/2, z)', '(1/2, x, z)',
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'8g': (7, ('(x, y, z)', '(-x, -y, z)', '(-y, x, z)',
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'100': {'2a': (4, ('(0, 0, z)', '(1/2, 1/2, z)'), 'hkl: h+k=2n'),
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'4c': (5, ('(x, x+1/2, z)', '(-x, -x+1/2, z)', '(-x+1/2, x, z)',
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'8d': (7, ('(x, y, z)', '(-x, -y, z)', '(-y, x, z)',
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'4c': (4, ('(0, 1/2, z)', '(1/2, 0, z+1/2)', '(0, 1/2, z+1/2)',
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'4d': (5, ('(x, x, z)', '(-x, -x, z)', '(-x, x, z+1/2)',
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'8e': (7, ('(x, y, z)', '(-x, -y, z)', '(-y, x, z+1/2)',
'(y, -x, z+1/2)', '(x, -y, z+1/2)', '(-x, y, z+1/2)',
'(-y, -x, z)', '(y, x, z)'), '0kl: l=2n, 00l: l=2n'
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'102': {'2a': (4, ('(0, 0, z)', '(1/2, 1/2, z+1/2)'), 'hkl: h+k+l=2n'),
'4b': (4, ('(0, 1/2, z)', '(0, 1/2, z+1/2)', '(1/2, 0, z+1/2)',
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'4c': (5, ('(x, x, z)', '(-x, -x, z)', '(-x+1/2, x+1/2, z+1/2)',
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'8d': (7, ('(x, y, z)', '(-x, -y, z)', '(-y+1/2, x+1/2, z+1/2)',
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'(-x+1/2, y+1/2, z+1/2)', '(-y, -x, z)', '(y, x, z)'
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'103': {'2a': (4, ('(0, 0, z)', '(0, 0, z+1/2)'), 'hkl: l=2n'),
'2b': (4, ('(1/2, 1/2, z)', '(1/2, 1/2, z+1/2)'), 'hkl: l=2n'),
'4c': (4, ('(0, 1/2, z)', '(1/2, 0, z)', '(0, 1/2, z+1/2)',
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'8d': (7, ('(x, y, z)', '(-x, -y, z)', '(-y, x, z)',
'(y, -x, z)', '(x, -y, z+1/2)', '(-x, y, z+1/2)',
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'4b': (4, ('(0, 1/2, z)', '(1/2, 0, z)', '(1/2, 0, z+1/2)',
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'8c': (7, ('(x, y, z)', '(-x, -y, z)', '(-y, x, z)',
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'105': {'2a': (4, ('(0, 0, z)', '(0, 0, z+1/2)'), 'hkl: l=2n'),
'2b': (4, ('(1/2, 1/2, z)', '(1/2, 1/2, z+1/2)'), 'hkl: l=2n'),
'2c': (4, ('(0, 1/2, z)', '(1/2, 0, z+1/2)'), 'hkl: h+k+l=2n'),
'4d': (5, ('(x, 0, z)', '(-x, 0, z)', '(0, x, z+1/2)',
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'4e': (5, ('(x, 1/2, z)', '(-x, 1/2, z)', '(1/2, x, z+1/2)',
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'8f': (7, ('(x, y, z)', '(-x, -y, z)', '(-y, x, z+1/2)',
'(y, -x, z+1/2)', '(x, -y, z)', '(-x, y, z)',
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'106': {'4a': (4, ('(0, 0, z)', '(0, 0, z+1/2)', '(1/2, 1/2, z)',
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'4b': (4, ('(0, 1/2, z)', '(1/2, 0, z+1/2)', '(1/2, 0, z)',
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'8c': (7, ('(x, y, z)', '(-x, -y, z)', '(-y, x, z+1/2)',
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'0kl: k=2n, hhl: l=2n, 00l: l=2n, h00: h=2n')},
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'(y+1/2, x+1/2, 1/2)', '(-y, -x, 0)',
'(-y+1/2, -x+1/2, 1/2)'), None),
'16m': (5, ('(x, x, z)', '(x+1/2, x+1/2, z+1/2)', '(-x, -x, z)',
'(-x+1/2, -x+1/2, z+1/2)', '(-x, x, z)',
'(-x+1/2, x+1/2, z+1/2)', '(x, -x, z)',
'(x+1/2, -x+1/2, z+1/2)', '(-x, x, -z)',
'(-x+1/2, x+1/2, -z+1/2)', '(x, -x, -z)',
'(x+1/2, -x+1/2, -z+1/2)', '(x, x, -z)',
'(x+1/2, x+1/2, -z+1/2)', '(-x, -x, -z)',
'(-x+1/2, -x+1/2, -z+1/2)'), None),
'16n': (6, ('(0, y, z)', '(1/2, y+1/2, z+1/2)', '(0, -y, z)',
'(1/2, -y+1/2, z+1/2)', '(-y, 0, z)',
'(-y+1/2, 1/2, z+1/2)', '(y, 0, z)',
'(y+1/2, 1/2, z+1/2)', '(0, y, -z)',
'(1/2, y+1/2, -z+1/2)', '(0, -y, -z)',
'(1/2, -y+1/2, -z+1/2)', '(y, 0, -z)',
'(y+1/2, 1/2, -z+1/2)', '(-y, 0, -z)',
'(-y+1/2, 1/2, -z+1/2)'), None),
'32o': (7, ('(x, y, z)', '(x+1/2, y+1/2, z+1/2)', '(-x, -y, z)',
'(-x+1/2, -y+1/2, z+1/2)', '(-y, x, z)',
'(-y+1/2, x+1/2, z+1/2)', '(y, -x, z)',
'(y+1/2, -x+1/2, z+1/2)', '(-x, y, -z)',
'(-x+1/2, y+1/2, -z+1/2)', '(x, -y, -z)',
'(x+1/2, -y+1/2, -z+1/2)', '(y, x, -z)',
'(y+1/2, x+1/2, -z+1/2)', '(-y, -x, -z)',
'(-y+1/2, -x+1/2, -z+1/2)', '(-x, -y, -z)',
'(-x+1/2, -y+1/2, -z+1/2)', '(x, y, -z)',
'(x+1/2, y+1/2, -z+1/2)', '(y, -x, -z)',
'(y+1/2, -x+1/2, -z+1/2)', '(-y, x, -z)',
'(-y+1/2, x+1/2, -z+1/2)', '(x, -y, z)',
'(x+1/2, -y+1/2, z+1/2)', '(-x, y, z)',
'(-x+1/2, y+1/2, z+1/2)', '(-y, -x, z)',
'(-y+1/2, -x+1/2, z+1/2)', '(y, x, z)',
'(y+1/2, x+1/2, z+1/2)'),
'hkl: h+k+l=2n, hk0: h+k=2n, 0kl: k+l=2n, hhl: l=2n, '
'00l: l=2n, h00: h=2n')},
'140': {'4a': (0, ('(0, 0, 1/4)', '(1/2, 1/2, 3/4)', '(0, 0, 3/4)',
'(1/2, 1/2, 1/4)'), 'hkl: l=2n'),
'4b': (0, ('(0, 1/2, 1/4)', '(1/2, 0, 3/4)', '(1/2, 0, 1/4)',
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'4c': (0, ('(0, 0, 0)', '(1/2, 1/2, 1/2)', '(0, 0, 1/2)',
'(1/2, 1/2, 0)'), 'hkl: l=2n'),
'4d': (0, ('(0, 1/2, 0)', '(1/2, 0, 1/2)', '(1/2, 0, 0)',
'(0, 1/2, 1/2)'), 'hkl: l=2n'),
'8e': (0, ('(1/4, 1/4, 1/4)', '(3/4, 3/4, 3/4)',
'(3/4, 3/4, 1/4)', '(1/4, 1/4, 3/4)',
'(3/4, 1/4, 1/4)', '(1/4, 3/4, 3/4)',
'(1/4, 3/4, 1/4)', '(3/4, 1/4, 3/4)'), 'hkl: k,l=2n'
),
'8f': (4, ('(0, 0, z)', '(1/2, 1/2, z+1/2)', '(0, 0, -z+1/2)',
'(1/2, 1/2, -z)', '(0, 0, -z)', '(1/2, 1/2, -z+1/2)',
'(0, 0, z+1/2)', '(1/2, 1/2, z)'), 'hkl: l=2n'),
'8g': (4, ('(0, 1/2, z)', '(1/2, 0, z+1/2)', '(1/2, 0, z)',
'(0, 1/2, z+1/2)', '(0, 1/2, -z+1/2)',
'(1/2, 0, -z)', '(1/2, 0, -z+1/2)', '(0, 1/2, -z)'),
'hkl: l=2n'),
'8h': (1, ('(x, x+1/2, 0)', '(x+1/2, x, 1/2)',
'(-x, -x+1/2, 0)', '(-x+1/2, -x, 1/2)',
'(-x+1/2, x, 0)', '(-x, x+1/2, 1/2)',
'(x+1/2, -x, 0)', '(x, -x+1/2, 1/2)'), None),
'16i': (1, ('(x, x, 1/4)', '(x+1/2, x+1/2, 3/4)',
'(-x, -x, 1/4)', '(-x+1/2, -x+1/2, 3/4)',
'(-x, x, 1/4)', '(-x+1/2, x+1/2, 3/4)',
'(x, -x, 1/4)', '(x+1/2, -x+1/2, 3/4)',
'(-x, -x, 3/4)', '(-x+1/2, -x+1/2, 1/4)',
'(x, x, 3/4)', '(x+1/2, x+1/2, 1/4)',
'(x, -x, 3/4)', '(x+1/2, -x+1/2, 1/4)',
'(-x, x, 3/4)', '(-x+1/2, x+1/2, 1/4)'), 'hkl: l=2n'
),
'16j': (1, ('(x, 0, 1/4)', '(x+1/2, 1/2, 3/4)', '(-x, 0, 1/4)',
'(-x+1/2, 1/2, 3/4)', '(0, x, 1/4)',
'(1/2, x+1/2, 3/4)', '(0, -x, 1/4)',
'(1/2, -x+1/2, 3/4)', '(-x, 0, 3/4)',
'(-x+1/2, 1/2, 1/4)', '(x, 0, 3/4)',
'(x+1/2, 1/2, 1/4)', '(0, -x, 3/4)',
'(1/2, -x+1/2, 1/4)', '(0, x, 3/4)',
'(1/2, x+1/2, 1/4)'), 'hkl: l=2n'),
'16k': (3, ('(x, y, 0)', '(x+1/2, y+1/2, 1/2)', '(-x, -y, 0)',
'(-x+1/2, -y+1/2, 1/2)', '(-y, x, 0)',
'(-y+1/2, x+1/2, 1/2)', '(y, -x, 0)',
'(y+1/2, -x+1/2, 1/2)', '(-x, y, 1/2)',
'(-x+1/2, y+1/2, 0)', '(x, -y, 1/2)',
'(x+1/2, -y+1/2, 0)', '(y, x, 1/2)',
'(y+1/2, x+1/2, 0)', '(-y, -x, 1/2)',
'(-y+1/2, -x+1/2, 0)'), None),
'16l': (5, ('(x, x+1/2, z)', '(x+1/2, x, z+1/2)',
'(-x, -x+1/2, z)', '(-x+1/2, -x, z+1/2)',
'(-x+1/2, x, z)', '(-x, x+1/2, z+1/2)',
'(x+1/2, -x, z)', '(x, -x+1/2, z+1/2)',
'(-x, x+1/2, -z+1/2)', '(-x+1/2, x, -z)',
'(x, -x+1/2, -z+1/2)', '(x+1/2, -x, -z)',
'(x+1/2, x, -z+1/2)', '(x, x+1/2, -z)',
'(-x+1/2, -x, -z+1/2)', '(-x, -x+1/2, -z)'), None),
'32m': (7, ('(x, y, z)', '(x+1/2, y+1/2, z+1/2)', '(-x, -y, z)',
'(-x+1/2, -y+1/2, z+1/2)', '(-y, x, z)',
'(-y+1/2, x+1/2, z+1/2)', '(y, -x, z)',
'(y+1/2, -x+1/2, z+1/2)', '(-x, y, -z+1/2)',
'(-x+1/2, y+1/2, -z)', '(x, -y, -z+1/2)',
'(x+1/2, -y+1/2, -z)', '(y, x, -z+1/2)',
'(y+1/2, x+1/2, -z)', '(-y, -x, -z+1/2)',
'(-y+1/2, -x+1/2, -z)', '(-x, -y, -z)',
'(-x+1/2, -y+1/2, -z+1/2)', '(x, y, -z)',
'(x+1/2, y+1/2, -z+1/2)', '(y, -x, -z)',
'(y+1/2, -x+1/2, -z+1/2)', '(-y, x, -z)',
'(-y+1/2, x+1/2, -z+1/2)', '(x, -y, z+1/2)',
'(x+1/2, -y+1/2, z)', '(-x, y, z+1/2)',
'(-x+1/2, y+1/2, z)', '(-y, -x, z+1/2)',
'(-y+1/2, -x+1/2, z)', '(y, x, z+1/2)',
'(y+1/2, x+1/2, z)'),
'hkl: h+k+l=2n, hk0: h+k=2n, 0kl: k,l=2n, hhl: l=2n, '
'00l: l=2n, h00: h=2n')},
'141:1': {'4a': (0, ('(0, 0, 0)', '(1/2, 1/2, 1/2)', '(0, 1/2, 1/4)',
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'4b': (0, ('(0, 0, 1/2)', '(1/2, 1/2, 0)', '(0, 1/2, 3/4)',
'(1/2, 0, 1/4)'), 'hkl: l=2n+1 or 2h+l=4n'),
'8c': (0, ('(0, 1/4, 1/8)', '(1/2, 3/4, 5/8)',
'(1/2, 1/4, 5/8)', '(0, 3/4, 1/8)',
'(3/4, 1/2, 3/8)', '(1/4, 0, 7/8)',
'(3/4, 0, 7/8)', '(1/4, 1/2, 3/8)'),
'hkl: l=2n+1 or h,k=2n, h+k+l=4n'),
'8d': (0, ('(0, 1/4, 5/8)', '(1/2, 3/4, 1/8)',
'(1/2, 1/4, 1/8)', '(0, 3/4, 5/8)',
'(3/4, 1/2, 7/8)', '(1/4, 0, 3/8)',
'(3/4, 0, 3/8)', '(1/4, 1/2, 7/8)'),
'hkl: l=2n+1 or h,k=2n, h+k+l=4n'),
'8e': (4, ('(0, 0, z)', '(1/2, 1/2, z+1/2)',
'(0, 1/2, z+1/4)', '(1/2, 0, z+3/4)',
'(1/2, 0, -z+3/4)', '(0, 1/2, -z+1/4)',
'(1/2, 1/2, -z+1/2)', '(0, 0, -z)'),
'hkl: l=2n+1 or 2h+l=4n'),
'16f': (1, ('(x, 1/4, 1/8)', '(x+1/2, 3/4, 5/8)',
'(-x+1/2, 1/4, 5/8)', '(-x, 3/4, 1/8)',
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'(3/4, -x, 7/8)', '(1/4, -x+1/2, 3/8)',
'(-x, 1/4, 1/8)', '(-x+1/2, 3/4, 5/8)',
'(x+1/2, 1/4, 5/8)', '(x, 3/4, 1/8)',
'(1/4, -x, 7/8)', '(3/4, -x+1/2, 3/8)',
'(1/4, x+1/2, 3/8)', '(3/4, x, 7/8)'),
'hkl: l=2n+1 or h=2n'),
'16g': (1, ('(x, x, 0)', '(x+1/2, x+1/2, 1/2)',
'(-x+1/2, -x+1/2, 1/2)', '(-x, -x, 0)',
'(-x, x+1/2, 1/4)', '(-x+1/2, x, 3/4)',
'(x+1/2, -x, 3/4)', '(x, -x+1/2, 1/4)',
'(-x, -x+1/2, 1/4)', '(-x+1/2, -x, 3/4)',
'(x+1/2, x, 3/4)', '(x, x+1/2, 1/4)',
'(x, -x, 0)', '(x+1/2, -x+1/2, 1/2)',
'(-x+1/2, x+1/2, 1/2)', '(-x, x, 0)'),
'hkl: l=2n+1 or 2h+l=4n'),
'16h': (6, ('(0, y, z)', '(1/2, y+1/2, z+1/2)',
'(1/2, -y+1/2, z+1/2)', '(0, -y, z)',
'(-y, 1/2, z+1/4)', '(-y+1/2, 0, z+3/4)',
'(y+1/2, 0, z+3/4)', '(y, 1/2, z+1/4)',
'(1/2, y, -z+3/4)', '(0, y+1/2, -z+1/4)',
'(0, -y+1/2, -z+1/4)', '(1/2, -y, -z+3/4)',
'(y+1/2, 1/2, -z+1/2)', '(y, 0, -z)',
'(-y, 0, -z)', '(-y+1/2, 1/2, -z+1/2)'), None),
'32i': (7, ('(x, y, z)', '(x+1/2, y+1/2, z+1/2)',
'(-x+1/2, -y+1/2, z+1/2)', '(-x, -y, z)',
'(-y, x+1/2, z+1/4)', '(-y+1/2, x, z+3/4)',
'(y+1/2, -x, z+3/4)', '(y, -x+1/2, z+1/4)',
'(-x+1/2, y, -z+3/4)', '(-x, y+1/2, -z+1/4)',
'(x, -y+1/2, -z+1/4)', '(x+1/2, -y, -z+3/4)',
'(y+1/2, x+1/2, -z+1/2)', '(y, x, -z)',
'(-y, -x, -z)', '(-y+1/2, -x+1/2, -z+1/2)',
'(-x, -y+1/2, -z+1/4)', '(-x+1/2, -y, -z+3/4)',
'(x+1/2, y, -z+3/4)', '(x, y+1/2, -z+1/4)',
'(y, -x, -z)', '(y+1/2, -x+1/2, -z+1/2)',
'(-y+1/2, x+1/2, -z+1/2)', '(-y, x, -z)',
'(x+1/2, -y+1/2, z+1/2)', '(x, -y, z)',
'(-x, y, z)', '(-x+1/2, y+1/2, z+1/2)',
'(-y+1/2, -x, z+3/4)', '(-y, -x+1/2, z+1/4)',
'(y, x+1/2, z+1/4)', '(y+1/2, x, z+3/4)'),
'hkl: h+k+l=2n, hk0: h,k=2n, 0kl: k+l=2n, '
'hhl: 2h+l=4n, 00l: l=4n, h00: h=2n, h-h0: h=2n')},
'141:2': {'4a': (0, ('(0, 3/4, 1/8)', '(1/2, 1/4, 5/8)',
'(1/2, 3/4, 3/8)', '(0, 1/4, 7/8)'), 'n/a'),
'4b': (0, ('(0, 1/4, 3/8)', '(1/2, 3/4, 7/8)',
'(0, 3/4, 5/8)', '(1/2, 1/4, 1/8)'), 'n/a'),
'8c': (0, ('(0, 0, 0)', '(1/2, 1/2, 1/2)', '(1/2, 0, 1/2)',
'(0, 1/2, 0)', '(1/4, 3/4, 1/4)',
'(3/4, 1/4, 3/4)', '(1/4, 1/4, 3/4)',
'(3/4, 3/4, 1/4)'), 'n/a'),
'8d': (0, ('(0, 0, 1/2)', '(1/2, 1/2, 0)', '(1/2, 0, 0)',
'(0, 1/2, 1/2)', '(1/4, 3/4, 3/4)',
'(3/4, 1/4, 1/4)', '(1/4, 1/4, 1/4)',
'(3/4, 3/4, 3/4)'), 'n/a'),
'8e': (4, ('(0, 1/4, z)', '(1/2, 3/4, z+1/2)',
'(0, 3/4, z+1/4)', '(1/2, 1/4, z+3/4)',
'(1/2, 1/4, -z+1/2)', '(0, 3/4, -z)',
'(1/2, 3/4, -z+1/4)', '(0, 1/4, -z+3/4)'), 'n/a'),
'16f': (1, ('(x, 0, 0)', '(x+1/2, 1/2, 1/2)',
'(-x+1/2, 0, 1/2)', '(-x, 1/2, 0)',
'(1/4, x+3/4, 1/4)', '(3/4, x+1/4, 3/4)',
'(1/4, -x+1/4, 3/4)', '(3/4, -x+3/4, 1/4)',
'(-x, 0, 0)', '(-x+1/2, 1/2, 1/2)',
'(x+1/2, 0, 1/2)', '(x, 1/2, 0)',
'(3/4, -x+1/4, 3/4)', '(1/4, -x+3/4, 1/4)',
'(3/4, x+3/4, 1/4)', '(1/4, x+1/4, 3/4)'), 'n/a'),
'16g': (1, ('(x, x+1/4, 7/8)', '(x+1/2, x+3/4, 3/8)',
'(-x+1/2, -x+3/4, 3/8)', '(-x, -x+1/4, 7/8)',
'(-x, x+3/4, 1/8)', '(-x+1/2, x+1/4, 5/8)',
'(x+1/2, -x+1/4, 5/8)', '(x, -x+3/4, 1/8)',
'(-x, -x+3/4, 1/8)', '(-x+1/2, -x+1/4, 5/8)',
'(x+1/2, x+1/4, 5/8)', '(x, x+3/4, 1/8)',
'(x, -x+1/4, 7/8)', '(x+1/2, -x+3/4, 3/8)',
'(-x+1/2, x+3/4, 3/8)', '(-x, x+1/4, 7/8)'), 'n/a'
),
'16h': (6, ('(0, y, z)', '(1/2, y+1/2, z+1/2)',
'(1/2, -y, z+1/2)', '(0, -y+1/2, z)',
'(-y+1/4, 3/4, z+1/4)', '(-y+3/4, 1/4, z+3/4)',
'(y+1/4, 1/4, z+3/4)', '(y+3/4, 3/4, z+1/4)',
'(1/2, y, -z+1/2)', '(0, y+1/2, -z)',
'(0, -y, -z)', '(1/2, -y+1/2, -z+1/2)',
'(y+1/4, 3/4, -z+1/4)', '(y+3/4, 1/4, -z+3/4)',
'(-y+1/4, 1/4, -z+3/4)', '(-y+3/4, 3/4, -z+1/4)'),
'n/a'),
'32i': (7, ('(x, y, z)', '(x+1/2, y+1/2, z+1/2)',
'(-x+1/2, -y, z+1/2)', '(-x, -y+1/2, z)',
'(-y+1/4, x+3/4, z+1/4)',
'(-y+3/4, x+1/4, z+3/4)',
'(y+1/4, -x+1/4, z+3/4)',
'(y+3/4, -x+3/4, z+1/4)', '(-x+1/2, y, -z+1/2)',
'(-x, y+1/2, -z)', '(x, -y, -z)',
'(x+1/2, -y+1/2, -z+1/2)',
'(y+1/4, x+3/4, -z+1/4)',
'(y+3/4, x+1/4, -z+3/4)',
'(-y+1/4, -x+1/4, -z+3/4)',
'(-y+3/4, -x+3/4, -z+1/4)', '(-x, -y, -z)',
'(-x+1/2, -y+1/2, -z+1/2)', '(x+1/2, y, -z+1/2)',
'(x, y+1/2, -z)', '(y+3/4, -x+1/4, -z+3/4)',
'(y+1/4, -x+3/4, -z+1/4)',
'(-y+3/4, x+3/4, -z+1/4)',
'(-y+1/4, x+1/4, -z+3/4)', '(x+1/2, -y, z+1/2)',
'(x, -y+1/2, z)', '(-x, y, z)',
'(-x+1/2, y+1/2, z+1/2)',
'(-y+3/4, -x+1/4, z+3/4)',
'(-y+1/4, -x+3/4, z+1/4)',
'(y+3/4, x+3/4, z+1/4)', '(y+1/4, x+1/4, z+3/4)'),
'n/a')},
'142:1': {'8a': (0, ('(0, 0, 0)', '(1/2, 1/2, 1/2)', '(0, 1/2, 1/4)',
'(1/2, 0, 3/4)', '(1/2, 0, 1/4)', '(0, 1/2, 3/4)',
'(1/2, 1/2, 0)', '(0, 0, 1/2)'), 'hkl: 2h+l=4n'),
'8b': (0, ('(0, 0, 1/4)', '(1/2, 1/2, 3/4)', '(0, 1/2, 1/2)',
'(1/2, 0, 0)', '(0, 1/2, 0)', '(1/2, 0, 1/2)',
'(0, 0, 3/4)', '(1/2, 1/2, 1/4)'), 'hkl: 2h+l=4n'),
'16c': (0, ('(0, 1/4, 1/8)', '(1/2, 3/4, 5/8)',
'(1/2, 1/4, 5/8)', '(0, 3/4, 1/8)',
'(3/4, 1/2, 3/8)', '(1/4, 0, 7/8)',
'(3/4, 0, 7/8)', '(1/4, 1/2, 3/8)',
'(1/2, 1/4, 1/8)', '(0, 3/4, 5/8)',
'(0, 1/4, 5/8)', '(1/2, 3/4, 1/8)',
'(3/4, 1/2, 7/8)', '(1/4, 0, 3/8)',
'(3/4, 0, 3/8)', '(1/4, 1/2, 7/8)'),
'hkl: h,k=2n, h+k+l=4n'),
'16d': (4, ('(0, 0, z)', '(1/2, 1/2, z+1/2)',
'(0, 1/2, z+1/4)', '(1/2, 0, z+3/4)',
'(1/2, 0, -z+1/4)', '(0, 1/2, -z+3/4)',
'(1/2, 1/2, -z)', '(0, 0, -z+1/2)',
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'6d': (7, ('(x, y, z)', '(-y, x-y, z)', '(-x+y, -x, z)',
'(y, x, z)', '(x-y, -y, z)', '(-x, -x+y, z)'), None
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'(-y, -x, z+1/2)', '(-x+y, y, z+1/2)',
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'2b': (4, ('(1/3, 2/3, z)', '(2/3, 1/3, z+1/2)'),
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'6c': (7, ('(x, y, z)', '(-y, x-y, z)', '(-x+y, -x, z)',
'(y, x, z+1/2)', '(x-y, -y, z+1/2)',
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'(x+1/3, 2*x+2/3, z+2/3)', '(-2*x, -x, z)',
'(-2*x+2/3, -x+1/3, z+1/3)',
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'(-x+y+2/3, y+1/3, z+1/3)',
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'(x+2/3, x-y+1/3, z+1/3)',
'(x+1/3, x-y+2/3, z+2/3)'),
'hkil: -h+k+l=3n, hki0: -h+k=3n, hh(-2h)l: l=3n, '
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'(x+2/3, x-y+1/3, z+5/6)',
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'hkil: -h+k+l=3n, hki0: -h+k=3n, hh(-2h)l: l=3n, '
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'(y, -x+y, -z)', '(x-y, x, -z)', '(-y, -x, z+1/2)',
'(-x+y, y, z+1/2)', '(x, x-y, z+1/2)'),
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'(1/2, 1/2, 0)', '(1/6, 5/6, 1/3)',
'(5/6, 1/6, 2/3)'), None),
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'(x+1/3, 2/3, 2/3)', '(0, x, 0)',
'(2/3, x+1/3, 1/3)', '(1/3, x+2/3, 2/3)',
'(-x, -x, 0)', '(-x+2/3, -x+1/3, 1/3)',
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'(-x+2/3, 1/3, 1/3)', '(-x+1/3, 2/3, 2/3)',
'(0, -x, 0)', '(2/3, -x+1/3, 1/3)',
'(1/3, -x+2/3, 2/3)', '(x, x, 0)',
'(x+2/3, x+1/3, 1/3)', '(x+1/3, x+2/3, 2/3)'), None
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'(x+1/3, 2/3, 1/6)', '(0, x, 1/2)',
'(2/3, x+1/3, 5/6)', '(1/3, x+2/3, 1/6)',
'(-x, -x, 1/2)', '(-x+2/3, -x+1/3, 5/6)',
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'(-x+2/3, 1/3, 5/6)', '(-x+1/3, 2/3, 1/6)',
'(0, -x, 1/2)', '(2/3, -x+1/3, 5/6)',
'(1/3, -x+2/3, 1/6)', '(x, x, 1/2)',
'(x+2/3, x+1/3, 5/6)', '(x+1/3, x+2/3, 1/6)'), None
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'(x+2/3, 2*x+1/3, z+1/3)',
'(x+1/3, 2*x+2/3, z+2/3)', '(-2*x, -x, z)',
'(-2*x+2/3, -x+1/3, z+1/3)',
'(-2*x+1/3, -x+2/3, z+2/3)', '(-x, x, -z)',
'(-x+2/3, x+1/3, -z+1/3)',
'(-x+1/3, x+2/3, -z+2/3)', '(2*x, x, -z)',
'(2*x+2/3, x+1/3, -z+1/3)',
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'(-x+2/3, -2*x+1/3, -z+1/3)',
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'(-x+y+2/3, -x+1/3, z+1/3)',
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'(y+2/3, x+1/3, -z+1/3)',
'(y+1/3, x+2/3, -z+2/3)', '(x-y, -y, -z)',
'(x-y+2/3, -y+1/3, -z+1/3)',
'(x-y+1/3, -y+2/3, -z+2/3)', '(-x, -x+y, -z)',
'(-x+2/3, -x+y+1/3, -z+1/3)',
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'(-x+2/3, -y+1/3, -z+1/3)',
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'(y+2/3, -x+y+1/3, -z+1/3)',
'(y+1/3, -x+y+2/3, -z+2/3)', '(x-y, x, -z)',
'(x-y+2/3, x+1/3, -z+1/3)',
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'(-x+y+2/3, y+1/3, z+1/3)',
'(-x+y+1/3, y+2/3, z+2/3)', '(x, x-y, z)',
'(x+2/3, x-y+1/3, z+1/3)',
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'hkil: -h+k+l=3n, hki0: -h+k=3n, hh(-2h)l: l=3n, '
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'hkl: h+k,h+l,k+l=2n, 0kl: k,l=2n, hhl: h+l=2n, '
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'(7/8, 3/8, 1/8)', '(7/8, 7/8, 5/8)',
'(3/8, 5/8, 3/8)', '(3/8, 1/8, 7/8)',
'(7/8, 5/8, 7/8)', '(7/8, 1/8, 3/8)',
'(5/8, 3/8, 3/8)', '(5/8, 7/8, 7/8)',
'(1/8, 3/8, 7/8)', '(1/8, 7/8, 3/8)'),
'hkl: h=2n+1 or h,k,l=4n+2 or h,k,l=4n'),
'32e': (1, ('(x, x, x)', '(x, x+1/2, x+1/2)',
'(x+1/2, x, x+1/2)', '(x+1/2, x+1/2, x)',
'(-x, -x, x)', '(-x, -x+1/2, x+1/2)',
'(-x+1/2, -x, x+1/2)', '(-x+1/2, -x+1/2, x)',
'(-x, x, -x)', '(-x, x+1/2, -x+1/2)',
'(-x+1/2, x, -x+1/2)', '(-x+1/2, x+1/2, -x)',
'(x, -x, -x)', '(x, -x+1/2, -x+1/2)',
'(x+1/2, -x, -x+1/2)', '(x+1/2, -x+1/2, -x)',
'(-x+1/4, -x+1/4, -x+1/4)',
'(-x+1/4, -x+3/4, -x+3/4)',
'(-x+3/4, -x+1/4, -x+3/4)',
'(-x+3/4, -x+3/4, -x+1/4)',
'(x+1/4, x+1/4, -x+1/4)',
'(x+1/4, x+3/4, -x+3/4)',
'(x+3/4, x+1/4, -x+3/4)',
'(x+3/4, x+3/4, -x+1/4)',
'(x+1/4, -x+1/4, x+1/4)',
'(x+1/4, -x+3/4, x+3/4)',
'(x+3/4, -x+1/4, x+3/4)',
'(x+3/4, -x+3/4, x+1/4)',
'(-x+1/4, x+1/4, x+1/4)',
'(-x+1/4, x+3/4, x+3/4)',
'(-x+3/4, x+1/4, x+3/4)',
'(-x+3/4, x+3/4, x+1/4)'), None),
'48f': (1, ('(x, 0, 0)', '(x, 1/2, 1/2)', '(x+1/2, 0, 1/2)',
'(x+1/2, 1/2, 0)', '(-x, 0, 0)', '(-x, 1/2, 1/2)',
'(-x+1/2, 0, 1/2)', '(-x+1/2, 1/2, 0)',
'(0, x, 0)', '(0, x+1/2, 1/2)', '(1/2, x, 1/2)',
'(1/2, x+1/2, 0)', '(0, -x, 0)',
'(0, -x+1/2, 1/2)', '(1/2, -x, 1/2)',
'(1/2, -x+1/2, 0)', '(0, 0, x)',
'(0, 1/2, x+1/2)', '(1/2, 0, x+1/2)',
'(1/2, 1/2, x)', '(0, 0, -x)', '(0, 1/2, -x+1/2)',
'(1/2, 0, -x+1/2)', '(1/2, 1/2, -x)',
'(-x+1/4, 1/4, 1/4)', '(-x+1/4, 3/4, 3/4)',
'(-x+3/4, 1/4, 3/4)', '(-x+3/4, 3/4, 1/4)',
'(x+1/4, 1/4, 1/4)', '(x+1/4, 3/4, 3/4)',
'(x+3/4, 1/4, 3/4)', '(x+3/4, 3/4, 1/4)',
'(1/4, -x+1/4, 1/4)', '(1/4, -x+3/4, 3/4)',
'(3/4, -x+1/4, 3/4)', '(3/4, -x+3/4, 1/4)',
'(1/4, x+1/4, 1/4)', '(1/4, x+3/4, 3/4)',
'(3/4, x+1/4, 3/4)', '(3/4, x+3/4, 1/4)',
'(1/4, 1/4, -x+1/4)', '(1/4, 3/4, -x+3/4)',
'(3/4, 1/4, -x+3/4)', '(3/4, 3/4, -x+1/4)',
'(1/4, 1/4, x+1/4)', '(1/4, 3/4, x+3/4)',
'(3/4, 1/4, x+3/4)', '(3/4, 3/4, x+1/4)'),
'hkl: h=2n+1 or h+k+l=4n'),
'96g': (7, ('(x, y, z)', '(x, y+1/2, z+1/2)',
'(x+1/2, y, z+1/2)', '(x+1/2, y+1/2, z)',
'(-x, -y, z)', '(-x, -y+1/2, z+1/2)',
'(-x+1/2, -y, z+1/2)', '(-x+1/2, -y+1/2, z)',
'(-x, y, -z)', '(-x, y+1/2, -z+1/2)',
'(-x+1/2, y, -z+1/2)', '(-x+1/2, y+1/2, -z)',
'(x, -y, -z)', '(x, -y+1/2, -z+1/2)',
'(x+1/2, -y, -z+1/2)', '(x+1/2, -y+1/2, -z)',
'(z, x, y)', '(z, x+1/2, y+1/2)',
'(z+1/2, x, y+1/2)', '(z+1/2, x+1/2, y)',
'(z, -x, -y)', '(z, -x+1/2, -y+1/2)',
'(z+1/2, -x, -y+1/2)', '(z+1/2, -x+1/2, -y)',
'(-z, -x, y)', '(-z, -x+1/2, y+1/2)',
'(-z+1/2, -x, y+1/2)', '(-z+1/2, -x+1/2, y)',
'(-z, x, -y)', '(-z, x+1/2, -y+1/2)',
'(-z+1/2, x, -y+1/2)', '(-z+1/2, x+1/2, -y)',
'(y, z, x)', '(y, z+1/2, x+1/2)',
'(y+1/2, z, x+1/2)', '(y+1/2, z+1/2, x)',
'(-y, z, -x)', '(-y, z+1/2, -x+1/2)',
'(-y+1/2, z, -x+1/2)', '(-y+1/2, z+1/2, -x)',
'(y, -z, -x)', '(y, -z+1/2, -x+1/2)',
'(y+1/2, -z, -x+1/2)', '(y+1/2, -z+1/2, -x)',
'(-y, -z, x)', '(-y, -z+1/2, x+1/2)',
'(-y+1/2, -z, x+1/2)', '(-y+1/2, -z+1/2, x)',
'(-x+1/4, -y+1/4, -z+1/4)',
'(-x+1/4, -y+3/4, -z+3/4)',
'(-x+3/4, -y+1/4, -z+3/4)',
'(-x+3/4, -y+3/4, -z+1/4)',
'(x+1/4, y+1/4, -z+1/4)',
'(x+1/4, y+3/4, -z+3/4)',
'(x+3/4, y+1/4, -z+3/4)',
'(x+3/4, y+3/4, -z+1/4)',
'(x+1/4, -y+1/4, z+1/4)',
'(x+1/4, -y+3/4, z+3/4)',
'(x+3/4, -y+1/4, z+3/4)',
'(x+3/4, -y+3/4, z+1/4)',
'(-x+1/4, y+1/4, z+1/4)',
'(-x+1/4, y+3/4, z+3/4)',
'(-x+3/4, y+1/4, z+3/4)',
'(-x+3/4, y+3/4, z+1/4)',
'(-z+1/4, -x+1/4, -y+1/4)',
'(-z+1/4, -x+3/4, -y+3/4)',
'(-z+3/4, -x+1/4, -y+3/4)',
'(-z+3/4, -x+3/4, -y+1/4)',
'(-z+1/4, x+1/4, y+1/4)',
'(-z+1/4, x+3/4, y+3/4)',
'(-z+3/4, x+1/4, y+3/4)',
'(-z+3/4, x+3/4, y+1/4)',
'(z+1/4, x+1/4, -y+1/4)',
'(z+1/4, x+3/4, -y+3/4)',
'(z+3/4, x+1/4, -y+3/4)',
'(z+3/4, x+3/4, -y+1/4)',
'(z+1/4, -x+1/4, y+1/4)',
'(z+1/4, -x+3/4, y+3/4)',
'(z+3/4, -x+1/4, y+3/4)',
'(z+3/4, -x+3/4, y+1/4)',
'(-y+1/4, -z+1/4, -x+1/4)',
'(-y+1/4, -z+3/4, -x+3/4)',
'(-y+3/4, -z+1/4, -x+3/4)',
'(-y+3/4, -z+3/4, -x+1/4)',
'(y+1/4, -z+1/4, x+1/4)',
'(y+1/4, -z+3/4, x+3/4)',
'(y+3/4, -z+1/4, x+3/4)',
'(y+3/4, -z+3/4, x+1/4)',
'(-y+1/4, z+1/4, x+1/4)',
'(-y+1/4, z+3/4, x+3/4)',
'(-y+3/4, z+1/4, x+3/4)',
'(-y+3/4, z+3/4, x+1/4)',
'(y+1/4, z+1/4, -x+1/4)',
'(y+1/4, z+3/4, -x+3/4)',
'(y+3/4, z+1/4, -x+3/4)',
'(y+3/4, z+3/4, -x+1/4)'),
'hkl: h+k,h+l,k+l=2n, 0kl: k+l=4n, k,l=2n, '
'hhl: h+l=2n, h00: h=4n')},
'203:2': {'8a': (0, ('(1/8, 1/8, 1/8)', '(1/8, 5/8, 5/8)',
'(5/8, 1/8, 5/8)', '(5/8, 5/8, 1/8)',
'(7/8, 7/8, 7/8)', '(7/8, 3/8, 3/8)',
'(3/8, 7/8, 3/8)', '(3/8, 3/8, 7/8)'), 'n/a'),
'8b': (0, ('(5/8, 5/8, 5/8)', '(5/8, 1/8, 1/8)',
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'(7/8, 3/8, 7/8)', '(7/8, 7/8, 3/8)'), 'n/a'),
'16c': (0, ('(0, 0, 0)', '(0, 1/2, 1/2)', '(1/2, 0, 1/2)',
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'(1/4, 1/4, 0)', '(3/4, 0, 3/4)',
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'(1/4, 1/2, 3/4)', '(0, 3/4, 3/4)',
'(0, 1/4, 1/4)', '(1/2, 3/4, 1/4)',
'(1/2, 1/4, 3/4)'), 'n/a'),
'16d': (0, ('(1/2, 1/2, 1/2)', '(1/2, 0, 0)', '(0, 1/2, 0)',
'(0, 0, 1/2)', '(1/4, 1/4, 1/2)', '(1/4, 3/4, 0)',
'(3/4, 1/4, 0)', '(3/4, 3/4, 1/2)',
'(1/4, 1/2, 1/4)', '(1/4, 0, 3/4)',
'(3/4, 1/2, 3/4)', '(3/4, 0, 1/4)',
'(1/2, 1/4, 1/4)', '(1/2, 3/4, 3/4)',
'(0, 1/4, 3/4)', '(0, 3/4, 1/4)'), 'n/a'),
'32e': (1, ('(x, x, x)', '(x, x+1/2, x+1/2)',
'(x+1/2, x, x+1/2)', '(x+1/2, x+1/2, x)',
'(-x+3/4, -x+3/4, x)', '(-x+3/4, -x+1/4, x+1/2)',
'(-x+1/4, -x+3/4, x+1/2)', '(-x+1/4, -x+1/4, x)',
'(-x+3/4, x, -x+3/4)', '(-x+3/4, x+1/2, -x+1/4)',
'(-x+1/4, x, -x+1/4)', '(-x+1/4, x+1/2, -x+3/4)',
'(x, -x+3/4, -x+3/4)', '(x, -x+1/4, -x+1/4)',
'(x+1/2, -x+3/4, -x+1/4)',
'(x+1/2, -x+1/4, -x+3/4)', '(-x, -x, -x)',
'(-x, -x+1/2, -x+1/2)', '(-x+1/2, -x, -x+1/2)',
'(-x+1/2, -x+1/2, -x)', '(x+1/4, x+1/4, -x)',
'(x+1/4, x+3/4, -x+1/2)',
'(x+3/4, x+1/4, -x+1/2)', '(x+3/4, x+3/4, -x)',
'(x+1/4, -x, x+1/4)', '(x+1/4, -x+1/2, x+3/4)',
'(x+3/4, -x, x+3/4)', '(x+3/4, -x+1/2, x+1/4)',
'(-x, x+1/4, x+1/4)', '(-x, x+3/4, x+3/4)',
'(-x+1/2, x+1/4, x+3/4)',
'(-x+1/2, x+3/4, x+1/4)'), 'n/a'),
'48f': (1, ('(x, 1/8, 1/8)', '(x, 5/8, 5/8)',
'(x+1/2, 1/8, 5/8)', '(x+1/2, 5/8, 1/8)',
'(-x+3/4, 5/8, 1/8)', '(-x+3/4, 1/8, 5/8)',
'(-x+1/4, 5/8, 5/8)', '(-x+1/4, 1/8, 1/8)',
'(1/8, x, 1/8)', '(1/8, x+1/2, 5/8)',
'(5/8, x, 5/8)', '(5/8, x+1/2, 1/8)',
'(1/8, -x+3/4, 5/8)', '(1/8, -x+1/4, 1/8)',
'(5/8, -x+3/4, 1/8)', '(5/8, -x+1/4, 5/8)',
'(1/8, 1/8, x)', '(1/8, 5/8, x+1/2)',
'(5/8, 1/8, x+1/2)', '(5/8, 5/8, x)',
'(5/8, 1/8, -x+3/4)', '(5/8, 5/8, -x+1/4)',
'(1/8, 1/8, -x+1/4)', '(1/8, 5/8, -x+3/4)',
'(-x, 7/8, 7/8)', '(-x, 3/8, 3/8)',
'(-x+1/2, 7/8, 3/8)', '(-x+1/2, 3/8, 7/8)',
'(x+1/4, 3/8, 7/8)', '(x+1/4, 7/8, 3/8)',
'(x+3/4, 3/8, 3/8)', '(x+3/4, 7/8, 7/8)',
'(7/8, -x, 7/8)', '(7/8, -x+1/2, 3/8)',
'(3/8, -x, 3/8)', '(3/8, -x+1/2, 7/8)',
'(7/8, x+1/4, 3/8)', '(7/8, x+3/4, 7/8)',
'(3/8, x+1/4, 7/8)', '(3/8, x+3/4, 3/8)',
'(7/8, 7/8, -x)', '(7/8, 3/8, -x+1/2)',
'(3/8, 7/8, -x+1/2)', '(3/8, 3/8, -x)',
'(3/8, 7/8, x+1/4)', '(3/8, 3/8, x+3/4)',
'(7/8, 7/8, x+3/4)', '(7/8, 3/8, x+1/4)'), 'n/a'),
'96g': (7, ('(x, y, z)', '(x, y+1/2, z+1/2)',
'(x+1/2, y, z+1/2)', '(x+1/2, y+1/2, z)',
'(-x+3/4, -y+3/4, z)', '(-x+3/4, -y+1/4, z+1/2)',
'(-x+1/4, -y+3/4, z+1/2)', '(-x+1/4, -y+1/4, z)',
'(-x+3/4, y, -z+3/4)', '(-x+3/4, y+1/2, -z+1/4)',
'(-x+1/4, y, -z+1/4)', '(-x+1/4, y+1/2, -z+3/4)',
'(x, -y+3/4, -z+3/4)', '(x, -y+1/4, -z+1/4)',
'(x+1/2, -y+3/4, -z+1/4)',
'(x+1/2, -y+1/4, -z+3/4)', '(z, x, y)',
'(z, x+1/2, y+1/2)', '(z+1/2, x, y+1/2)',
'(z+1/2, x+1/2, y)', '(z, -x+3/4, -y+3/4)',
'(z, -x+1/4, -y+1/4)', '(z+1/2, -x+3/4, -y+1/4)',
'(z+1/2, -x+1/4, -y+3/4)', '(-z+3/4, -x+3/4, y)',
'(-z+3/4, -x+1/4, y+1/2)',
'(-z+1/4, -x+3/4, y+1/2)', '(-z+1/4, -x+1/4, y)',
'(-z+3/4, x, -y+3/4)', '(-z+3/4, x+1/2, -y+1/4)',
'(-z+1/4, x, -y+1/4)', '(-z+1/4, x+1/2, -y+3/4)',
'(y, z, x)', '(y, z+1/2, x+1/2)',
'(y+1/2, z, x+1/2)', '(y+1/2, z+1/2, x)',
'(-y+3/4, z, -x+3/4)', '(-y+3/4, z+1/2, -x+1/4)',
'(-y+1/4, z, -x+1/4)', '(-y+1/4, z+1/2, -x+3/4)',
'(y, -z+3/4, -x+3/4)', '(y, -z+1/4, -x+1/4)',
'(y+1/2, -z+3/4, -x+1/4)',
'(y+1/2, -z+1/4, -x+3/4)', '(-y+3/4, -z+3/4, x)',
'(-y+3/4, -z+1/4, x+1/2)',
'(-y+1/4, -z+3/4, x+1/2)', '(-y+1/4, -z+1/4, x)',
'(-x, -y, -z)', '(-x, -y+1/2, -z+1/2)',
'(-x+1/2, -y, -z+1/2)', '(-x+1/2, -y+1/2, -z)',
'(x+1/4, y+1/4, -z)', '(x+1/4, y+3/4, -z+1/2)',
'(x+3/4, y+1/4, -z+1/2)', '(x+3/4, y+3/4, -z)',
'(x+1/4, -y, z+1/4)', '(x+1/4, -y+1/2, z+3/4)',
'(x+3/4, -y, z+3/4)', '(x+3/4, -y+1/2, z+1/4)',
'(-x, y+1/4, z+1/4)', '(-x, y+3/4, z+3/4)',
'(-x+1/2, y+1/4, z+3/4)',
'(-x+1/2, y+3/4, z+1/4)', '(-z, -x, -y)',
'(-z, -x+1/2, -y+1/2)', '(-z+1/2, -x, -y+1/2)',
'(-z+1/2, -x+1/2, -y)', '(-z, x+1/4, y+1/4)',
'(-z, x+3/4, y+3/4)', '(-z+1/2, x+1/4, y+3/4)',
'(-z+1/2, x+3/4, y+1/4)', '(z+1/4, x+1/4, -y)',
'(z+1/4, x+3/4, -y+1/2)',
'(z+3/4, x+1/4, -y+1/2)', '(z+3/4, x+3/4, -y)',
'(z+1/4, -x, y+1/4)', '(z+1/4, -x+1/2, y+3/4)',
'(z+3/4, -x, y+3/4)', '(z+3/4, -x+1/2, y+1/4)',
'(-y, -z, -x)', '(-y, -z+1/2, -x+1/2)',
'(-y+1/2, -z, -x+1/2)', '(-y+1/2, -z+1/2, -x)',
'(y+1/4, -z, x+1/4)', '(y+1/4, -z+1/2, x+3/4)',
'(y+3/4, -z, x+3/4)', '(y+3/4, -z+1/2, x+1/4)',
'(-y, z+1/4, x+1/4)', '(-y, z+3/4, x+3/4)',
'(-y+1/2, z+1/4, x+3/4)',
'(-y+1/2, z+3/4, x+1/4)', '(y+1/4, z+1/4, -x)',
'(y+1/4, z+3/4, -x+1/2)',
'(y+3/4, z+1/4, -x+1/2)', '(y+3/4, z+3/4, -x)'),
'n/a')},
'204': {'2a': (0, ('(0, 0, 0)', '(1/2, 1/2, 1/2)'), None),
'6b': (0, ('(0, 1/2, 1/2)', '(1/2, 0, 0)', '(1/2, 0, 1/2)',
'(0, 1/2, 0)', '(1/2, 1/2, 0)', '(0, 0, 1/2)'), None
),
'8c': (0, ('(1/4, 1/4, 1/4)', '(3/4, 3/4, 3/4)',
'(3/4, 3/4, 1/4)', '(1/4, 1/4, 3/4)',
'(3/4, 1/4, 3/4)', '(1/4, 3/4, 1/4)',
'(1/4, 3/4, 3/4)', '(3/4, 1/4, 1/4)'), 'hkl: k,l=2n'
),
'12d': (1, ('(x, 0, 0)', '(x+1/2, 1/2, 1/2)', '(-x, 0, 0)',
'(-x+1/2, 1/2, 1/2)', '(0, x, 0)',
'(1/2, x+1/2, 1/2)', '(0, -x, 0)',
'(1/2, -x+1/2, 1/2)', '(0, 0, x)',
'(1/2, 1/2, x+1/2)', '(0, 0, -x)',
'(1/2, 1/2, -x+1/2)'), None),
'12e': (1, ('(x, 0, 1/2)', '(x+1/2, 1/2, 0)', '(-x, 0, 1/2)',
'(-x+1/2, 1/2, 0)', '(1/2, x, 0)',
'(0, x+1/2, 1/2)', '(1/2, -x, 0)',
'(0, -x+1/2, 1/2)', '(0, 1/2, x)',
'(1/2, 0, x+1/2)', '(0, 1/2, -x)',
'(1/2, 0, -x+1/2)'), None),
'16f': (1, ('(x, x, x)', '(x+1/2, x+1/2, x+1/2)', '(-x, -x, x)',
'(-x+1/2, -x+1/2, x+1/2)', '(-x, x, -x)',
'(-x+1/2, x+1/2, -x+1/2)', '(x, -x, -x)',
'(x+1/2, -x+1/2, -x+1/2)', '(-x, -x, -x)',
'(-x+1/2, -x+1/2, -x+1/2)', '(x, x, -x)',
'(x+1/2, x+1/2, -x+1/2)', '(x, -x, x)',
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'(y+1/2, -z+1/2, 1/2)', '(-y, -z, 0)',
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'(-z+1/2, -x+1/2, y+1/2)', '(-z, x, -y)',
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'(-y, y, 1/2)', '(y, -y, 1/2)', '(-y, -y, 1/2)'),
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'(y, y+1/2, 1/4)', '(-y, y+1/2, 3/4)',
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'48g': (2, ('(0, y, y)', '(0, y+1/2, y+1/2)', '(1/2, y, y+1/2)',
'(1/2, y+1/2, y)', '(0, -y, y)',
'(0, -y+1/2, y+1/2)', '(1/2, -y, y+1/2)',
'(1/2, -y+1/2, y)', '(0, y, -y)',
'(0, y+1/2, -y+1/2)', '(1/2, y, -y+1/2)',
'(1/2, y+1/2, -y)', '(0, -y, -y)',
'(0, -y+1/2, -y+1/2)', '(1/2, -y, -y+1/2)',
'(1/2, -y+1/2, -y)', '(y, 0, y)', '(y, 1/2, y+1/2)',
'(y+1/2, 0, y+1/2)', '(y+1/2, 1/2, y)',
'(y, 0, -y)', '(y, 1/2, -y+1/2)',
'(y+1/2, 0, -y+1/2)', '(y+1/2, 1/2, -y)',
'(-y, 0, y)', '(-y, 1/2, y+1/2)',
'(-y+1/2, 0, y+1/2)', '(-y+1/2, 1/2, y)',
'(-y, 0, -y)', '(-y, 1/2, -y+1/2)',
'(-y+1/2, 0, -y+1/2)', '(-y+1/2, 1/2, -y)',
'(y, y, 0)', '(y, y+1/2, 1/2)', '(y+1/2, y, 1/2)',
'(y+1/2, y+1/2, 0)', '(-y, y, 0)',
'(-y, y+1/2, 1/2)', '(-y+1/2, y, 1/2)',
'(-y+1/2, y+1/2, 0)', '(y, -y, 0)',
'(y, -y+1/2, 1/2)', '(y+1/2, -y, 1/2)',
'(y+1/2, -y+1/2, 0)', '(-y, -y, 0)',
'(-y, -y+1/2, 1/2)', '(-y+1/2, -y, 1/2)',
'(-y+1/2, -y+1/2, 0)'), None),
'48h': (2, ('(1/2, y, y)', '(1/2, y+1/2, y+1/2)',
'(0, y, y+1/2)', '(0, y+1/2, y)', '(1/2, -y, y)',
'(1/2, -y+1/2, y+1/2)', '(0, -y, y+1/2)',
'(0, -y+1/2, y)', '(1/2, y, -y)',
'(1/2, y+1/2, -y+1/2)', '(0, y, -y+1/2)',
'(0, y+1/2, -y)', '(1/2, -y, -y)',
'(1/2, -y+1/2, -y+1/2)', '(0, -y, -y+1/2)',
'(0, -y+1/2, -y)', '(y, 1/2, y)', '(y, 0, y+1/2)',
'(y+1/2, 1/2, y+1/2)', '(y+1/2, 0, y)',
'(y, 1/2, -y)', '(y, 0, -y+1/2)',
'(y+1/2, 1/2, -y+1/2)', '(y+1/2, 0, -y)',
'(-y, 1/2, y)', '(-y, 0, y+1/2)',
'(-y+1/2, 1/2, y+1/2)', '(-y+1/2, 0, y)',
'(-y, 1/2, -y)', '(-y, 0, -y+1/2)',
'(-y+1/2, 1/2, -y+1/2)', '(-y+1/2, 0, -y)',
'(y, y, 1/2)', '(y, y+1/2, 0)', '(y+1/2, y, 0)',
'(y+1/2, y+1/2, 1/2)', '(-y, y, 1/2)',
'(-y, y+1/2, 0)', '(-y+1/2, y, 0)',
'(-y+1/2, y+1/2, 1/2)', '(y, -y, 1/2)',
'(y, -y+1/2, 0)', '(y+1/2, -y, 0)',
'(y+1/2, -y+1/2, 1/2)', '(-y, -y, 1/2)',
'(-y, -y+1/2, 0)', '(-y+1/2, -y, 0)',
'(-y+1/2, -y+1/2, 1/2)'), None),
'48i': (1, ('(x, 1/4, 1/4)', '(x, 3/4, 3/4)',
'(x+1/2, 1/4, 3/4)', '(x+1/2, 3/4, 1/4)',
'(-x, 3/4, 1/4)', '(-x, 1/4, 3/4)',
'(-x+1/2, 3/4, 3/4)', '(-x+1/2, 1/4, 1/4)',
'(1/4, x, 1/4)', '(1/4, x+1/2, 3/4)',
'(3/4, x, 3/4)', '(3/4, x+1/2, 1/4)',
'(1/4, -x, 3/4)', '(1/4, -x+1/2, 1/4)',
'(3/4, -x, 1/4)', '(3/4, -x+1/2, 3/4)',
'(1/4, 1/4, x)', '(1/4, 3/4, x+1/2)',
'(3/4, 1/4, x+1/2)', '(3/4, 3/4, x)',
'(3/4, 1/4, -x)', '(3/4, 3/4, -x+1/2)',
'(1/4, 1/4, -x+1/2)', '(1/4, 3/4, -x)',
'(1/4, x, 3/4)', '(1/4, x+1/2, 1/4)',
'(3/4, x, 1/4)', '(3/4, x+1/2, 3/4)',
'(3/4, -x, 3/4)', '(3/4, -x+1/2, 1/4)',
'(1/4, -x, 1/4)', '(1/4, -x+1/2, 3/4)',
'(x, 1/4, 3/4)', '(x, 3/4, 1/4)',
'(x+1/2, 1/4, 1/4)', '(x+1/2, 3/4, 3/4)',
'(-x, 1/4, 1/4)', '(-x, 3/4, 3/4)',
'(-x+1/2, 1/4, 3/4)', '(-x+1/2, 3/4, 1/4)',
'(1/4, 1/4, -x)', '(1/4, 3/4, -x+1/2)',
'(3/4, 1/4, -x+1/2)', '(3/4, 3/4, -x)',
'(1/4, 3/4, x)', '(1/4, 1/4, x+1/2)',
'(3/4, 3/4, x+1/2)', '(3/4, 1/4, x)'), 'hkl: h=2n'),
'96j': (7, ('(x, y, z)', '(x, y+1/2, z+1/2)',
'(x+1/2, y, z+1/2)', '(x+1/2, y+1/2, z)',
'(-x, -y, z)', '(-x, -y+1/2, z+1/2)',
'(-x+1/2, -y, z+1/2)', '(-x+1/2, -y+1/2, z)',
'(-x, y, -z)', '(-x, y+1/2, -z+1/2)',
'(-x+1/2, y, -z+1/2)', '(-x+1/2, y+1/2, -z)',
'(x, -y, -z)', '(x, -y+1/2, -z+1/2)',
'(x+1/2, -y, -z+1/2)', '(x+1/2, -y+1/2, -z)',
'(z, x, y)', '(z, x+1/2, y+1/2)',
'(z+1/2, x, y+1/2)', '(z+1/2, x+1/2, y)',
'(z, -x, -y)', '(z, -x+1/2, -y+1/2)',
'(z+1/2, -x, -y+1/2)', '(z+1/2, -x+1/2, -y)',
'(-z, -x, y)', '(-z, -x+1/2, y+1/2)',
'(-z+1/2, -x, y+1/2)', '(-z+1/2, -x+1/2, y)',
'(-z, x, -y)', '(-z, x+1/2, -y+1/2)',
'(-z+1/2, x, -y+1/2)', '(-z+1/2, x+1/2, -y)',
'(y, z, x)', '(y, z+1/2, x+1/2)',
'(y+1/2, z, x+1/2)', '(y+1/2, z+1/2, x)',
'(-y, z, -x)', '(-y, z+1/2, -x+1/2)',
'(-y+1/2, z, -x+1/2)', '(-y+1/2, z+1/2, -x)',
'(y, -z, -x)', '(y, -z+1/2, -x+1/2)',
'(y+1/2, -z, -x+1/2)', '(y+1/2, -z+1/2, -x)',
'(-y, -z, x)', '(-y, -z+1/2, x+1/2)',
'(-y+1/2, -z, x+1/2)', '(-y+1/2, -z+1/2, x)',
'(y, x, -z)', '(y, x+1/2, -z+1/2)',
'(y+1/2, x, -z+1/2)', '(y+1/2, x+1/2, -z)',
'(-y, -x, -z)', '(-y, -x+1/2, -z+1/2)',
'(-y+1/2, -x, -z+1/2)', '(-y+1/2, -x+1/2, -z)',
'(y, -x, z)', '(y, -x+1/2, z+1/2)',
'(y+1/2, -x, z+1/2)', '(y+1/2, -x+1/2, z)',
'(-y, x, z)', '(-y, x+1/2, z+1/2)',
'(-y+1/2, x, z+1/2)', '(-y+1/2, x+1/2, z)',
'(x, z, -y)', '(x, z+1/2, -y+1/2)',
'(x+1/2, z, -y+1/2)', '(x+1/2, z+1/2, -y)',
'(-x, z, y)', '(-x, z+1/2, y+1/2)',
'(-x+1/2, z, y+1/2)', '(-x+1/2, z+1/2, y)',
'(-x, -z, -y)', '(-x, -z+1/2, -y+1/2)',
'(-x+1/2, -z, -y+1/2)', '(-x+1/2, -z+1/2, -y)',
'(x, -z, y)', '(x, -z+1/2, y+1/2)',
'(x+1/2, -z, y+1/2)', '(x+1/2, -z+1/2, y)',
'(z, y, -x)', '(z, y+1/2, -x+1/2)',
'(z+1/2, y, -x+1/2)', '(z+1/2, y+1/2, -x)',
'(z, -y, x)', '(z, -y+1/2, x+1/2)',
'(z+1/2, -y, x+1/2)', '(z+1/2, -y+1/2, x)',
'(-z, y, x)', '(-z, y+1/2, x+1/2)',
'(-z+1/2, y, x+1/2)', '(-z+1/2, y+1/2, x)',
'(-z, -y, -x)', '(-z, -y+1/2, -x+1/2)',
'(-z+1/2, -y, -x+1/2)', '(-z+1/2, -y+1/2, -x)'),
'hkl: h+k,h+l,k+l=2n, 0kl: k,l=2n, hhl: h+l=2n, '
'h00: h=2n')},
'210': {'8a': (0, ('(0, 0, 0)', '(0, 1/2, 1/2)', '(1/2, 0, 1/2)',
'(1/2, 1/2, 0)', '(3/4, 1/4, 3/4)',
'(3/4, 3/4, 1/4)', '(1/4, 1/4, 1/4)',
'(1/4, 3/4, 3/4)'), 'hkl: h=2n+1 or h+k+l=4n'),
'8b': (0, ('(1/2, 1/2, 1/2)', '(1/2, 0, 0)', '(0, 1/2, 0)',
'(0, 0, 1/2)', '(1/4, 3/4, 1/4)', '(1/4, 1/4, 3/4)',
'(3/4, 3/4, 3/4)', '(3/4, 1/4, 1/4)'),
'hkl: h=2n+1 or h+k+l=4n'),
'16c': (0, ('(1/8, 1/8, 1/8)', '(1/8, 5/8, 5/8)',
'(5/8, 1/8, 5/8)', '(5/8, 5/8, 1/8)',
'(7/8, 3/8, 5/8)', '(7/8, 7/8, 1/8)',
'(3/8, 3/8, 1/8)', '(3/8, 7/8, 5/8)',
'(3/8, 5/8, 7/8)', '(3/8, 1/8, 3/8)',
'(7/8, 5/8, 3/8)', '(7/8, 1/8, 7/8)',
'(5/8, 7/8, 3/8)', '(5/8, 3/8, 7/8)',
'(1/8, 7/8, 7/8)', '(1/8, 3/8, 3/8)'),
'hkl: h=2n+1 or h,k,l=4n+2 or h,k,l=4n'),
'16d': (0, ('(5/8, 5/8, 5/8)', '(5/8, 1/8, 1/8)',
'(1/8, 5/8, 1/8)', '(1/8, 1/8, 5/8)',
'(3/8, 7/8, 1/8)', '(3/8, 3/8, 5/8)',
'(7/8, 7/8, 5/8)', '(7/8, 3/8, 1/8)',
'(7/8, 1/8, 3/8)', '(7/8, 5/8, 7/8)',
'(3/8, 1/8, 7/8)', '(3/8, 5/8, 3/8)',
'(1/8, 3/8, 7/8)', '(1/8, 7/8, 3/8)',
'(5/8, 3/8, 3/8)', '(5/8, 7/8, 7/8)'),
'hkl: h=2n+1 or h,k,l=4n+2 or h,k,l=4n'),
'32e': (1, ('(x, x, x)', '(x, x+1/2, x+1/2)',
'(x+1/2, x, x+1/2)', '(x+1/2, x+1/2, x)',
'(-x, -x+1/2, x+1/2)', '(-x, -x, x)',
'(-x+1/2, -x+1/2, x)', '(-x+1/2, -x, x+1/2)',
'(-x+1/2, x+1/2, -x)', '(-x+1/2, x, -x+1/2)',
'(-x, x+1/2, -x+1/2)', '(-x, x, -x)',
'(x+1/2, -x, -x+1/2)', '(x+1/2, -x+1/2, -x)',
'(x, -x, -x)', '(x, -x+1/2, -x+1/2)',
'(x+3/4, x+1/4, -x+3/4)', '(x+3/4, x+3/4, -x+1/4)',
'(x+1/4, x+1/4, -x+1/4)', '(x+1/4, x+3/4, -x+3/4)',
'(-x+1/4, -x+1/4, -x+1/4)',
'(-x+1/4, -x+3/4, -x+3/4)',
'(-x+3/4, -x+1/4, -x+3/4)',
'(-x+3/4, -x+3/4, -x+1/4)',
'(x+1/4, -x+3/4, x+3/4)', '(x+1/4, -x+1/4, x+1/4)',
'(x+3/4, -x+3/4, x+1/4)', '(x+3/4, -x+1/4, x+3/4)',
'(-x+3/4, x+3/4, x+1/4)', '(-x+3/4, x+1/4, x+3/4)',
'(-x+1/4, x+3/4, x+3/4)', '(-x+1/4, x+1/4, x+1/4)'),
'0kl: k+l=4n'),
'48f': (1, ('(x, 0, 0)', '(x, 1/2, 1/2)', '(x+1/2, 0, 1/2)',
'(x+1/2, 1/2, 0)', '(-x, 1/2, 1/2)', '(-x, 0, 0)',
'(-x+1/2, 1/2, 0)', '(-x+1/2, 0, 1/2)', '(0, x, 0)',
'(0, x+1/2, 1/2)', '(1/2, x, 1/2)',
'(1/2, x+1/2, 0)', '(1/2, -x, 1/2)',
'(1/2, -x+1/2, 0)', '(0, -x, 0)',
'(0, -x+1/2, 1/2)', '(0, 0, x)', '(0, 1/2, x+1/2)',
'(1/2, 0, x+1/2)', '(1/2, 1/2, x)',
'(1/2, 1/2, -x)', '(1/2, 0, -x+1/2)',
'(0, 1/2, -x+1/2)', '(0, 0, -x)',
'(3/4, x+1/4, 3/4)', '(3/4, x+3/4, 1/4)',
'(1/4, x+1/4, 1/4)', '(1/4, x+3/4, 3/4)',
'(1/4, -x+1/4, 1/4)', '(1/4, -x+3/4, 3/4)',
'(3/4, -x+1/4, 3/4)', '(3/4, -x+3/4, 1/4)',
'(x+3/4, 1/4, 3/4)', '(x+3/4, 3/4, 1/4)',
'(x+1/4, 1/4, 1/4)', '(x+1/4, 3/4, 3/4)',
'(-x+3/4, 3/4, 1/4)', '(-x+3/4, 1/4, 3/4)',
'(-x+1/4, 3/4, 3/4)', '(-x+1/4, 1/4, 1/4)',
'(3/4, 1/4, -x+3/4)', '(3/4, 3/4, -x+1/4)',
'(1/4, 1/4, -x+1/4)', '(1/4, 3/4, -x+3/4)',
'(1/4, 3/4, x+3/4)', '(1/4, 1/4, x+1/4)',
'(3/4, 3/4, x+1/4)', '(3/4, 1/4, x+3/4)'),
'hkl: h=2n+1 or h+k+l=4n'),
'48g': (2, ('(1/8, y, -y+1/4)', '(1/8, y+1/2, -y+3/4)',
'(5/8, y, -y+3/4)', '(5/8, y+1/2, -y+1/4)',
'(7/8, -y+1/2, -y+3/4)', '(7/8, -y, -y+1/4)',
'(3/8, -y+1/2, -y+1/4)', '(3/8, -y, -y+3/4)',
'(3/8, y+1/2, y+3/4)', '(3/8, y, y+1/4)',
'(7/8, y+1/2, y+1/4)', '(7/8, y, y+3/4)',
'(5/8, -y, y+1/4)', '(5/8, -y+1/2, y+3/4)',
'(1/8, -y, y+3/4)', '(1/8, -y+1/2, y+1/4)',
'(-y+1/4, 1/8, y)', '(-y+1/4, 5/8, y+1/2)',
'(-y+3/4, 1/8, y+1/2)', '(-y+3/4, 5/8, y)',
'(-y+3/4, 7/8, -y+1/2)', '(-y+3/4, 3/8, -y)',
'(-y+1/4, 7/8, -y)', '(-y+1/4, 3/8, -y+1/2)',
'(y+3/4, 3/8, y+1/2)', '(y+3/4, 7/8, y)',
'(y+1/4, 3/8, y)', '(y+1/4, 7/8, y+1/2)',
'(y+1/4, 5/8, -y)', '(y+1/4, 1/8, -y+1/2)',
'(y+3/4, 5/8, -y+1/2)', '(y+3/4, 1/8, -y)',
'(y, -y+1/4, 1/8)', '(y, -y+3/4, 5/8)',
'(y+1/2, -y+1/4, 5/8)', '(y+1/2, -y+3/4, 1/8)',
'(-y+1/2, -y+3/4, 7/8)', '(-y+1/2, -y+1/4, 3/8)',
'(-y, -y+3/4, 3/8)', '(-y, -y+1/4, 7/8)',
'(y+1/2, y+3/4, 3/8)', '(y+1/2, y+1/4, 7/8)',
'(y, y+3/4, 7/8)', '(y, y+1/4, 3/8)',
'(-y, y+1/4, 5/8)', '(-y, y+3/4, 1/8)',
'(-y+1/2, y+1/4, 1/8)', '(-y+1/2, y+3/4, 5/8)'), None
),
'96h': (7, ('(x, y, z)', '(x, y+1/2, z+1/2)',
'(x+1/2, y, z+1/2)', '(x+1/2, y+1/2, z)',
'(-x, -y+1/2, z+1/2)', '(-x, -y, z)',
'(-x+1/2, -y+1/2, z)', '(-x+1/2, -y, z+1/2)',
'(-x+1/2, y+1/2, -z)', '(-x+1/2, y, -z+1/2)',
'(-x, y+1/2, -z+1/2)', '(-x, y, -z)',
'(x+1/2, -y, -z+1/2)', '(x+1/2, -y+1/2, -z)',
'(x, -y, -z)', '(x, -y+1/2, -z+1/2)', '(z, x, y)',
'(z, x+1/2, y+1/2)', '(z+1/2, x, y+1/2)',
'(z+1/2, x+1/2, y)', '(z+1/2, -x, -y+1/2)',
'(z+1/2, -x+1/2, -y)', '(z, -x, -y)',
'(z, -x+1/2, -y+1/2)', '(-z, -x+1/2, y+1/2)',
'(-z, -x, y)', '(-z+1/2, -x+1/2, y)',
'(-z+1/2, -x, y+1/2)', '(-z+1/2, x+1/2, -y)',
'(-z+1/2, x, -y+1/2)', '(-z, x+1/2, -y+1/2)',
'(-z, x, -y)', '(y, z, x)', '(y, z+1/2, x+1/2)',
'(y+1/2, z, x+1/2)', '(y+1/2, z+1/2, x)',
'(-y+1/2, z+1/2, -x)', '(-y+1/2, z, -x+1/2)',
'(-y, z+1/2, -x+1/2)', '(-y, z, -x)',
'(y+1/2, -z, -x+1/2)', '(y+1/2, -z+1/2, -x)',
'(y, -z, -x)', '(y, -z+1/2, -x+1/2)',
'(-y, -z+1/2, x+1/2)', '(-y, -z, x)',
'(-y+1/2, -z+1/2, x)', '(-y+1/2, -z, x+1/2)',
'(y+3/4, x+1/4, -z+3/4)', '(y+3/4, x+3/4, -z+1/4)',
'(y+1/4, x+1/4, -z+1/4)', '(y+1/4, x+3/4, -z+3/4)',
'(-y+1/4, -x+1/4, -z+1/4)',
'(-y+1/4, -x+3/4, -z+3/4)',
'(-y+3/4, -x+1/4, -z+3/4)',
'(-y+3/4, -x+3/4, -z+1/4)',
'(y+1/4, -x+3/4, z+3/4)', '(y+1/4, -x+1/4, z+1/4)',
'(y+3/4, -x+3/4, z+1/4)', '(y+3/4, -x+1/4, z+3/4)',
'(-y+3/4, x+3/4, z+1/4)', '(-y+3/4, x+1/4, z+3/4)',
'(-y+1/4, x+3/4, z+3/4)', '(-y+1/4, x+1/4, z+1/4)',
'(x+3/4, z+1/4, -y+3/4)', '(x+3/4, z+3/4, -y+1/4)',
'(x+1/4, z+1/4, -y+1/4)', '(x+1/4, z+3/4, -y+3/4)',
'(-x+3/4, z+3/4, y+1/4)', '(-x+3/4, z+1/4, y+3/4)',
'(-x+1/4, z+3/4, y+3/4)', '(-x+1/4, z+1/4, y+1/4)',
'(-x+1/4, -z+1/4, -y+1/4)',
'(-x+1/4, -z+3/4, -y+3/4)',
'(-x+3/4, -z+1/4, -y+3/4)',
'(-x+3/4, -z+3/4, -y+1/4)',
'(x+1/4, -z+3/4, y+3/4)', '(x+1/4, -z+1/4, y+1/4)',
'(x+3/4, -z+3/4, y+1/4)', '(x+3/4, -z+1/4, y+3/4)',
'(z+3/4, y+1/4, -x+3/4)', '(z+3/4, y+3/4, -x+1/4)',
'(z+1/4, y+1/4, -x+1/4)', '(z+1/4, y+3/4, -x+3/4)',
'(z+1/4, -y+3/4, x+3/4)', '(z+1/4, -y+1/4, x+1/4)',
'(z+3/4, -y+3/4, x+1/4)', '(z+3/4, -y+1/4, x+3/4)',
'(-z+3/4, y+3/4, x+1/4)', '(-z+3/4, y+1/4, x+3/4)',
'(-z+1/4, y+3/4, x+3/4)', '(-z+1/4, y+1/4, x+1/4)',
'(-z+1/4, -y+1/4, -x+1/4)',
'(-z+1/4, -y+3/4, -x+3/4)',
'(-z+3/4, -y+1/4, -x+3/4)',
'(-z+3/4, -y+3/4, -x+1/4)'),
'hkl: h+k=2n, h+l,k+l=2n, 0kl: k,l=2n, hhl: h+l=2n, '
'h00: h=4n')},
'211': {'2a': (0, ('(0, 0, 0)', '(1/2, 1/2, 1/2)'), None),
'6b': (0, ('(0, 1/2, 1/2)', '(1/2, 0, 0)', '(1/2, 0, 1/2)',
'(0, 1/2, 0)', '(1/2, 1/2, 0)', '(0, 0, 1/2)'), None
),
'8c': (0, ('(1/4, 1/4, 1/4)', '(3/4, 3/4, 3/4)',
'(3/4, 3/4, 1/4)', '(1/4, 1/4, 3/4)',
'(3/4, 1/4, 3/4)', '(1/4, 3/4, 1/4)',
'(1/4, 3/4, 3/4)', '(3/4, 1/4, 1/4)'), 'hkl: k,l=2n'
),
'12d': (0, ('(1/4, 1/2, 0)', '(3/4, 0, 1/2)', '(3/4, 1/2, 0)',
'(1/4, 0, 1/2)', '(0, 1/4, 1/2)', '(1/2, 3/4, 0)',
'(0, 3/4, 1/2)', '(1/2, 1/4, 0)', '(1/2, 0, 1/4)',
'(0, 1/2, 3/4)', '(1/2, 0, 3/4)', '(0, 1/2, 1/4)'),
None),
'12e': (1, ('(x, 0, 0)', '(x+1/2, 1/2, 1/2)', '(-x, 0, 0)',
'(-x+1/2, 1/2, 1/2)', '(0, x, 0)',
'(1/2, x+1/2, 1/2)', '(0, -x, 0)',
'(1/2, -x+1/2, 1/2)', '(0, 0, x)',
'(1/2, 1/2, x+1/2)', '(0, 0, -x)',
'(1/2, 1/2, -x+1/2)'), None),
'16f': (1, ('(x, x, x)', '(x+1/2, x+1/2, x+1/2)', '(-x, -x, x)',
'(-x+1/2, -x+1/2, x+1/2)', '(-x, x, -x)',
'(-x+1/2, x+1/2, -x+1/2)', '(x, -x, -x)',
'(x+1/2, -x+1/2, -x+1/2)', '(x, x, -x)',
'(x+1/2, x+1/2, -x+1/2)', '(-x, -x, -x)',
'(-x+1/2, -x+1/2, -x+1/2)', '(x, -x, x)',
'(x+1/2, -x+1/2, x+1/2)', '(-x, x, x)',
'(-x+1/2, x+1/2, x+1/2)'), None),
'24g': (1, ('(x, 1/2, 0)', '(x+1/2, 0, 1/2)', '(-x, 1/2, 0)',
'(-x+1/2, 0, 1/2)', '(0, x, 1/2)',
'(1/2, x+1/2, 0)', '(0, -x, 1/2)',
'(1/2, -x+1/2, 0)', '(1/2, 0, x)',
'(0, 1/2, x+1/2)', '(1/2, 0, -x)',
'(0, 1/2, -x+1/2)', '(1/2, x, 0)',
'(0, x+1/2, 1/2)', '(1/2, -x, 0)',
'(0, -x+1/2, 1/2)', '(x, 0, 1/2)',
'(x+1/2, 1/2, 0)', '(-x, 0, 1/2)',
'(-x+1/2, 1/2, 0)', '(0, 1/2, -x)',
'(1/2, 0, -x+1/2)', '(0, 1/2, x)',
'(1/2, 0, x+1/2)'), None),
'24h': (2, ('(0, y, y)', '(1/2, y+1/2, y+1/2)', '(0, -y, y)',
'(1/2, -y+1/2, y+1/2)', '(0, y, -y)',
'(1/2, y+1/2, -y+1/2)', '(0, -y, -y)',
'(1/2, -y+1/2, -y+1/2)', '(y, 0, y)',
'(y+1/2, 1/2, y+1/2)', '(y, 0, -y)',
'(y+1/2, 1/2, -y+1/2)', '(-y, 0, y)',
'(-y+1/2, 1/2, y+1/2)', '(-y, 0, -y)',
'(-y+1/2, 1/2, -y+1/2)', '(y, y, 0)',
'(y+1/2, y+1/2, 1/2)', '(-y, y, 0)',
'(-y+1/2, y+1/2, 1/2)', '(y, -y, 0)',
'(y+1/2, -y+1/2, 1/2)', '(-y, -y, 0)',
'(-y+1/2, -y+1/2, 1/2)'), None),
'24i': (2, ('(1/4, y, -y+1/2)', '(3/4, y+1/2, -y)',
'(3/4, -y, -y+1/2)', '(1/4, -y+1/2, -y)',
'(3/4, y, y+1/2)', '(1/4, y+1/2, y)',
'(1/4, -y, y+1/2)', '(3/4, -y+1/2, y)',
'(-y+1/2, 1/4, y)', '(-y, 3/4, y+1/2)',
'(-y+1/2, 3/4, -y)', '(-y, 1/4, -y+1/2)',
'(y+1/2, 3/4, y)', '(y, 1/4, y+1/2)',
'(y+1/2, 1/4, -y)', '(y, 3/4, -y+1/2)',
'(y, -y+1/2, 1/4)', '(y+1/2, -y, 3/4)',
'(-y, -y+1/2, 3/4)', '(-y+1/2, -y, 1/4)',
'(y, y+1/2, 3/4)', '(y+1/2, y, 1/4)',
'(-y, y+1/2, 1/4)', '(-y+1/2, y, 3/4)'), None),
'48j': (7, ('(x, y, z)', '(x+1/2, y+1/2, z+1/2)', '(-x, -y, z)',
'(-x+1/2, -y+1/2, z+1/2)', '(-x, y, -z)',
'(-x+1/2, y+1/2, -z+1/2)', '(x, -y, -z)',
'(x+1/2, -y+1/2, -z+1/2)', '(z, x, y)',
'(z+1/2, x+1/2, y+1/2)', '(z, -x, -y)',
'(z+1/2, -x+1/2, -y+1/2)', '(-z, -x, y)',
'(-z+1/2, -x+1/2, y+1/2)', '(-z, x, -y)',
'(-z+1/2, x+1/2, -y+1/2)', '(y, z, x)',
'(y+1/2, z+1/2, x+1/2)', '(-y, z, -x)',
'(-y+1/2, z+1/2, -x+1/2)', '(y, -z, -x)',
'(y+1/2, -z+1/2, -x+1/2)', '(-y, -z, x)',
'(-y+1/2, -z+1/2, x+1/2)', '(y, x, -z)',
'(y+1/2, x+1/2, -z+1/2)', '(-y, -x, -z)',
'(-y+1/2, -x+1/2, -z+1/2)', '(y, -x, z)',
'(y+1/2, -x+1/2, z+1/2)', '(-y, x, z)',
'(-y+1/2, x+1/2, z+1/2)', '(x, z, -y)',
'(x+1/2, z+1/2, -y+1/2)', '(-x, z, y)',
'(-x+1/2, z+1/2, y+1/2)', '(-x, -z, -y)',
'(-x+1/2, -z+1/2, -y+1/2)', '(x, -z, y)',
'(x+1/2, -z+1/2, y+1/2)', '(z, y, -x)',
'(z+1/2, y+1/2, -x+1/2)', '(z, -y, x)',
'(z+1/2, -y+1/2, x+1/2)', '(-z, y, x)',
'(-z+1/2, y+1/2, x+1/2)', '(-z, -y, -x)',
'(-z+1/2, -y+1/2, -x+1/2)'),
'hkl: h+k+l=2n, 0kl: k+l=2n, hhl: l=2n, h00: h=2n')},
'212': {'4a': (0, ('(1/8, 1/8, 1/8)', '(3/8, 7/8, 5/8)',
'(7/8, 5/8, 3/8)', '(5/8, 3/8, 7/8)'),
'hkl: h,k=2n+1 or h=2n+1, k=4n, '
'l=4n+2 or h,k,l=4n+2 or h,k,l=4n'),
'4b': (0, ('(5/8, 5/8, 5/8)', '(7/8, 3/8, 1/8)',
'(3/8, 1/8, 7/8)', '(1/8, 7/8, 3/8)'),
'hkl: h,k=2n+1 or h=2n+1, k=4n, '
'l=4n+2 or h,k,l=4n+2 or h,k,l=4n'),
'8c': (1, ('(x, x, x)', '(-x+1/2, -x, x+1/2)',
'(-x, x+1/2, -x+1/2)', '(x+1/2, -x+1/2, -x)',
'(x+1/4, x+3/4, -x+3/4)', '(-x+1/4, -x+1/4, -x+1/4)',
'(x+3/4, -x+3/4, x+1/4)', '(-x+3/4, x+1/4, x+3/4)'),
'0kl: k=2n+1 or l=2n+1 or k+l=4n'),
'12d': (2, ('(1/8, y, -y+1/4)', '(3/8, -y, -y+3/4)',
'(7/8, y+1/2, y+1/4)', '(5/8, -y+1/2, y+3/4)',
'(-y+1/4, 1/8, y)', '(-y+3/4, 3/8, -y)',
'(y+1/4, 7/8, y+1/2)', '(y+3/4, 5/8, -y+1/2)',
'(y, -y+1/4, 1/8)', '(-y, -y+3/4, 3/8)',
'(y+1/2, y+1/4, 7/8)', '(-y+1/2, y+3/4, 5/8)'), None
),
'24e': (7, ('(x, y, z)', '(-x+1/2, -y, z+1/2)',
'(-x, y+1/2, -z+1/2)', '(x+1/2, -y+1/2, -z)',
'(z, x, y)', '(z+1/2, -x+1/2, -y)',
'(-z+1/2, -x, y+1/2)', '(-z, x+1/2, -y+1/2)',
'(y, z, x)', '(-y, z+1/2, -x+1/2)',
'(y+1/2, -z+1/2, -x)', '(-y+1/2, -z, x+1/2)',
'(y+1/4, x+3/4, -z+3/4)',
'(-y+1/4, -x+1/4, -z+1/4)',
'(y+3/4, -x+3/4, z+1/4)', '(-y+3/4, x+1/4, z+3/4)',
'(x+1/4, z+3/4, -y+3/4)', '(-x+3/4, z+1/4, y+3/4)',
'(-x+1/4, -z+1/4, -y+1/4)',
'(x+3/4, -z+3/4, y+1/4)', '(z+1/4, y+3/4, -x+3/4)',
'(z+3/4, -y+3/4, x+1/4)', '(-z+3/4, y+1/4, x+3/4)',
'(-z+1/4, -y+1/4, -x+1/4)'), 'h00: h=4n')},
'213': {'4a': (0, ('(3/8, 3/8, 3/8)', '(1/8, 5/8, 7/8)',
'(5/8, 7/8, 1/8)', '(7/8, 1/8, 5/8)'),
'hkl: h,k=2n+1 or h=2n+1, k=4n, '
'l=4n+2 or h,k,l=4n+2 or h,k,l=4n'),
'4b': (0, ('(7/8, 7/8, 7/8)', '(5/8, 1/8, 3/8)',
'(1/8, 3/8, 5/8)', '(3/8, 5/8, 1/8)'),
'hkl: h,k=2n+1 or h=2n+1, k=4n, '
'l=4n+2 or h,k,l=4n+2 or h,k,l=4n'),
'8c': (1, ('(x, x, x)', '(-x+1/2, -x, x+1/2)',
'(-x, x+1/2, -x+1/2)', '(x+1/2, -x+1/2, -x)',
'(x+3/4, x+1/4, -x+1/4)', '(-x+3/4, -x+3/4, -x+3/4)',
'(x+1/4, -x+1/4, x+3/4)', '(-x+1/4, x+3/4, x+1/4)'),
'0kl: k=2n+1 or l=2n+1 or k+l=4n'),
'12d': (2, ('(1/8, y, y+1/4)', '(3/8, -y, y+3/4)',
'(7/8, y+1/2, -y+1/4)', '(5/8, -y+1/2, -y+3/4)',
'(y+1/4, 1/8, y)', '(y+3/4, 3/8, -y)',
'(-y+1/4, 7/8, y+1/2)', '(-y+3/4, 5/8, -y+1/2)',
'(y, y+1/4, 1/8)', '(-y, y+3/4, 3/8)',
'(y+1/2, -y+1/4, 7/8)', '(-y+1/2, -y+3/4, 5/8)'),
None),
'24e': (7, ('(x, y, z)', '(-x+1/2, -y, z+1/2)',
'(-x, y+1/2, -z+1/2)', '(x+1/2, -y+1/2, -z)',
'(z, x, y)', '(z+1/2, -x+1/2, -y)',
'(-z+1/2, -x, y+1/2)', '(-z, x+1/2, -y+1/2)',
'(y, z, x)', '(-y, z+1/2, -x+1/2)',
'(y+1/2, -z+1/2, -x)', '(-y+1/2, -z, x+1/2)',
'(y+3/4, x+1/4, -z+1/4)',
'(-y+3/4, -x+3/4, -z+3/4)',
'(y+1/4, -x+1/4, z+3/4)', '(-y+1/4, x+3/4, z+1/4)',
'(x+3/4, z+1/4, -y+1/4)', '(-x+1/4, z+3/4, y+1/4)',
'(-x+3/4, -z+3/4, -y+3/4)',
'(x+1/4, -z+1/4, y+3/4)', '(z+3/4, y+1/4, -x+1/4)',
'(z+1/4, -y+1/4, x+3/4)', '(-z+1/4, y+3/4, x+1/4)',
'(-z+3/4, -y+3/4, -x+3/4)'), 'h00: h=4n')},
'214': {'8a': (0, ('(1/8, 1/8, 1/8)', '(5/8, 5/8, 5/8)',
'(3/8, 7/8, 5/8)', '(7/8, 3/8, 1/8)',
'(7/8, 5/8, 3/8)', '(3/8, 1/8, 7/8)',
'(5/8, 3/8, 7/8)', '(1/8, 7/8, 3/8)'),
'hkl: h=2n+1 or h,k,l=4n+2 or h,k,l=4n'),
'8b': (0, ('(7/8, 7/8, 7/8)', '(3/8, 3/8, 3/8)',
'(5/8, 1/8, 3/8)', '(1/8, 5/8, 7/8)',
'(1/8, 3/8, 5/8)', '(5/8, 7/8, 1/8)',
'(3/8, 5/8, 1/8)', '(7/8, 1/8, 5/8)'),
'hkl: h=2n+1 or h,k,l=4n+2 or h,k,l=4n'),
'12c': (0, ('(1/8, 0, 1/4)', '(5/8, 1/2, 3/4)', '(3/8, 0, 3/4)',
'(7/8, 1/2, 1/4)', '(1/4, 1/8, 0)',
'(3/4, 5/8, 1/2)', '(3/4, 3/8, 0)',
'(1/4, 7/8, 1/2)', '(0, 1/4, 1/8)',
'(1/2, 3/4, 5/8)', '(0, 3/4, 3/8)',
'(1/2, 1/4, 7/8)'),
'hkl: h,k=2n, h+k+l=4n or h,k=2n+1, '
'l=4n+2 or h=8n, k=8n+4, '
'h+k+l=4n+2 or h,k=8n+1, l=4n or h=8n+1, '
'k=8n-1, l=4n or h,k=8n+3, l=4n or '
'h=8n+3, k=8n-3, l=4n'),
'12d': (0, ('(5/8, 0, 1/4)', '(1/8, 1/2, 3/4)', '(7/8, 0, 3/4)',
'(3/8, 1/2, 1/4)', '(1/4, 5/8, 0)',
'(3/4, 1/8, 1/2)', '(3/4, 7/8, 0)',
'(1/4, 3/8, 1/2)', '(0, 1/4, 5/8)',
'(1/2, 3/4, 1/8)', '(0, 3/4, 7/8)',
'(1/2, 1/4, 3/8)'),
'hkl: h,k=2n, h+k+l=4n or h,k=2n+1, '
'l=4n+2 or h=8n, k=8n+4, '
'h+k+l=4n+2 or h,k=8n+1, l=4n or h=8n+1, '
'k=8n-1, l=4n or h,k=8n+3, l=4n or '
'h=8n+3, k=8n-3, l=4n'),
'16e': (1, ('(x, x, x)', '(x+1/2, x+1/2, x+1/2)',
'(-x+1/2, -x, x+1/2)', '(-x, -x+1/2, x)',
'(-x, x+1/2, -x+1/2)', '(-x+1/2, x, -x)',
'(x+1/2, -x+1/2, -x)', '(x, -x, -x+1/2)',
'(x+3/4, x+1/4, -x+1/4)', '(x+1/4, x+3/4, -x+3/4)',
'(-x+3/4, -x+3/4, -x+3/4)',
'(-x+1/4, -x+1/4, -x+1/4)',
'(x+1/4, -x+1/4, x+3/4)', '(x+3/4, -x+3/4, x+1/4)',
'(-x+1/4, x+3/4, x+1/4)', '(-x+3/4, x+1/4, x+3/4)'),
'0kl: k=2n+1 or k+l=4n'),
'24f': (1, ('(x, 0, 1/4)', '(x+1/2, 1/2, 3/4)',
'(-x+1/2, 0, 3/4)', '(-x, 1/2, 1/4)', '(1/4, x, 0)',
'(3/4, x+1/2, 1/2)', '(3/4, -x+1/2, 0)',
'(1/4, -x, 1/2)', '(0, 1/4, x)',
'(1/2, 3/4, x+1/2)', '(0, 3/4, -x+1/2)',
'(1/2, 1/4, -x)', '(3/4, x+1/4, 0)',
'(1/4, x+3/4, 1/2)', '(3/4, -x+3/4, 1/2)',
'(1/4, -x+1/4, 0)', '(x+3/4, 1/2, 1/4)',
'(x+1/4, 0, 3/4)', '(-x+1/4, 0, 1/4)',
'(-x+3/4, 1/2, 3/4)', '(0, 1/4, -x+1/4)',
'(1/2, 3/4, -x+3/4)', '(1/2, 1/4, x+3/4)',
'(0, 3/4, x+1/4)'),
'hkl: h=2n+1 or h=4n, hhl: h=2n+1 or h+k+l=4n'),
'24g': (2, ('(1/8, y, y+1/4)', '(5/8, y+1/2, y+3/4)',
'(3/8, -y, y+3/4)', '(7/8, -y+1/2, y+1/4)',
'(7/8, y+1/2, -y+1/4)', '(3/8, y, -y+3/4)',
'(5/8, -y+1/2, -y+3/4)', '(1/8, -y, -y+1/4)',
'(y+1/4, 1/8, y)', '(y+3/4, 5/8, y+1/2)',
'(y+3/4, 3/8, -y)', '(y+1/4, 7/8, -y+1/2)',
'(-y+1/4, 7/8, y+1/2)', '(-y+3/4, 3/8, y)',
'(-y+3/4, 5/8, -y+1/2)', '(-y+1/4, 1/8, -y)',
'(y, y+1/4, 1/8)', '(y+1/2, y+3/4, 5/8)',
'(-y, y+3/4, 3/8)', '(-y+1/2, y+1/4, 7/8)',
'(y+1/2, -y+1/4, 7/8)', '(y, -y+3/4, 3/8)',
'(-y+1/2, -y+3/4, 5/8)', '(-y, -y+1/4, 1/8)'), None
),
'24h': (2, ('(1/8, y, -y+1/4)', '(5/8, y+1/2, -y+3/4)',
'(3/8, -y, -y+3/4)', '(7/8, -y+1/2, -y+1/4)',
'(7/8, y+1/2, y+1/4)', '(3/8, y, y+3/4)',
'(5/8, -y+1/2, y+3/4)', '(1/8, -y, y+1/4)',
'(-y+1/4, 1/8, y)', '(-y+3/4, 5/8, y+1/2)',
'(-y+3/4, 3/8, -y)', '(-y+1/4, 7/8, -y+1/2)',
'(y+1/4, 7/8, y+1/2)', '(y+3/4, 3/8, y)',
'(y+3/4, 5/8, -y+1/2)', '(y+1/4, 1/8, -y)',
'(y, -y+1/4, 1/8)', '(y+1/2, -y+3/4, 5/8)',
'(-y, -y+3/4, 3/8)', '(-y+1/2, -y+1/4, 7/8)',
'(y+1/2, y+1/4, 7/8)', '(y, y+3/4, 3/8)',
'(-y+1/2, y+3/4, 5/8)', '(-y, y+1/4, 1/8)'), None),
'48i': (7, ('(x, y, z)', '(x+1/2, y+1/2, z+1/2)',
'(-x+1/2, -y, z+1/2)', '(-x, -y+1/2, z)',
'(-x, y+1/2, -z+1/2)', '(-x+1/2, y, -z)',
'(x+1/2, -y+1/2, -z)', '(x, -y, -z+1/2)',
'(z, x, y)', '(z+1/2, x+1/2, y+1/2)',
'(z+1/2, -x+1/2, -y)', '(z, -x, -y+1/2)',
'(-z+1/2, -x, y+1/2)', '(-z, -x+1/2, y)',
'(-z, x+1/2, -y+1/2)', '(-z+1/2, x, -y)',
'(y, z, x)', '(y+1/2, z+1/2, x+1/2)',
'(-y, z+1/2, -x+1/2)', '(-y+1/2, z, -x)',
'(y+1/2, -z+1/2, -x)', '(y, -z, -x+1/2)',
'(-y+1/2, -z, x+1/2)', '(-y, -z+1/2, x)',
'(y+3/4, x+1/4, -z+1/4)', '(y+1/4, x+3/4, -z+3/4)',
'(-y+3/4, -x+3/4, -z+3/4)',
'(-y+1/4, -x+1/4, -z+1/4)',
'(y+1/4, -x+1/4, z+3/4)', '(y+3/4, -x+3/4, z+1/4)',
'(-y+1/4, x+3/4, z+1/4)', '(-y+3/4, x+1/4, z+3/4)',
'(x+3/4, z+1/4, -y+1/4)', '(x+1/4, z+3/4, -y+3/4)',
'(-x+1/4, z+3/4, y+1/4)', '(-x+3/4, z+1/4, y+3/4)',
'(-x+3/4, -z+3/4, -y+3/4)',
'(-x+1/4, -z+1/4, -y+1/4)',
'(x+1/4, -z+1/4, y+3/4)', '(x+3/4, -z+3/4, y+1/4)',
'(z+3/4, y+1/4, -x+1/4)', '(z+1/4, y+3/4, -x+3/4)',
'(z+1/4, -y+1/4, x+3/4)', '(z+3/4, -y+3/4, x+1/4)',
'(-z+1/4, y+3/4, x+1/4)', '(-z+3/4, y+1/4, x+3/4)',
'(-z+3/4, -y+3/4, -x+3/4)',
'(-z+1/4, -y+1/4, -x+1/4)'),
'hkl: h+k+l=2n, 0kl: k+l=2n, hhl: l=2n, h00: h=4n')},
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'3c': (0, ('(0, 1/2, 1/2)', '(1/2, 0, 1/2)', '(1/2, 1/2, 0)'),
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'4e': (1, ('(x, x, x)', '(-x, -x, x)', '(-x, x, -x)',
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None),
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'(-x, 0, 1/2)', '(0, 1/2, x)', '(0, 1/2, -x)'), None
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'12i': (5, ('(x, x, z)', '(-x, -x, z)', '(-x, x, -z)',
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'(-x, z, -x)', '(x, -z, -x)', '(-x, -z, x)'), None),
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'(y, x, z)', '(-y, -x, z)', '(y, -x, -z)',
'(-y, x, -z)', '(x, z, y)', '(-x, z, -y)',
'(-x, -z, y)', '(x, -z, -y)', '(z, y, x)',
'(z, -y, -x)', '(-z, y, -x)', '(-z, -y, x)'), None
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'(3/4, 1/4, 3/4)', '(3/4, 3/4, 1/4)'), None),
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'(-x+1/2, -x, x+1/2)', '(-x+1/2, -x+1/2, x)',
'(-x, x, -x)', '(-x, x+1/2, -x+1/2)',
'(-x+1/2, x, -x+1/2)', '(-x+1/2, x+1/2, -x)',
'(x, -x, -x)', '(x, -x+1/2, -x+1/2)',
'(x+1/2, -x, -x+1/2)', '(x+1/2, -x+1/2, -x)'), None
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'(1/2, 1/2, x)', '(0, 0, -x)', '(0, 1/2, -x+1/2)',
'(1/2, 0, -x+1/2)', '(1/2, 1/2, -x)'), None),
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'(x+1/2, 1/4, 3/4)', '(x+1/2, 3/4, 1/4)',
'(-x, 3/4, 1/4)', '(-x, 1/4, 3/4)',
'(-x+1/2, 3/4, 3/4)', '(-x+1/2, 1/4, 1/4)',
'(1/4, x, 1/4)', '(1/4, x+1/2, 3/4)',
'(3/4, x, 3/4)', '(3/4, x+1/2, 1/4)',
'(1/4, -x, 3/4)', '(1/4, -x+1/2, 1/4)',
'(3/4, -x, 1/4)', '(3/4, -x+1/2, 3/4)',
'(1/4, 1/4, x)', '(1/4, 3/4, x+1/2)',
'(3/4, 1/4, x+1/2)', '(3/4, 3/4, x)',
'(3/4, 1/4, -x)', '(3/4, 3/4, -x+1/2)',
'(1/4, 1/4, -x+1/2)', '(1/4, 3/4, -x)'), None),
'48h': (5, ('(x, x, z)', '(x, x+1/2, z+1/2)',
'(x+1/2, x, z+1/2)', '(x+1/2, x+1/2, z)',
'(-x, -x, z)', '(-x, -x+1/2, z+1/2)',
'(-x+1/2, -x, z+1/2)', '(-x+1/2, -x+1/2, z)',
'(-x, x, -z)', '(-x, x+1/2, -z+1/2)',
'(-x+1/2, x, -z+1/2)', '(-x+1/2, x+1/2, -z)',
'(x, -x, -z)', '(x, -x+1/2, -z+1/2)',
'(x+1/2, -x, -z+1/2)', '(x+1/2, -x+1/2, -z)',
'(z, x, x)', '(z, x+1/2, x+1/2)',
'(z+1/2, x, x+1/2)', '(z+1/2, x+1/2, x)',
'(z, -x, -x)', '(z, -x+1/2, -x+1/2)',
'(z+1/2, -x, -x+1/2)', '(z+1/2, -x+1/2, -x)',
'(-z, -x, x)', '(-z, -x+1/2, x+1/2)',
'(-z+1/2, -x, x+1/2)', '(-z+1/2, -x+1/2, x)',
'(-z, x, -x)', '(-z, x+1/2, -x+1/2)',
'(-z+1/2, x, -x+1/2)', '(-z+1/2, x+1/2, -x)',
'(x, z, x)', '(x, z+1/2, x+1/2)',
'(x+1/2, z, x+1/2)', '(x+1/2, z+1/2, x)',
'(-x, z, -x)', '(-x, z+1/2, -x+1/2)',
'(-x+1/2, z, -x+1/2)', '(-x+1/2, z+1/2, -x)',
'(x, -z, -x)', '(x, -z+1/2, -x+1/2)',
'(x+1/2, -z, -x+1/2)', '(x+1/2, -z+1/2, -x)',
'(-x, -z, x)', '(-x, -z+1/2, x+1/2)',
'(-x+1/2, -z, x+1/2)', '(-x+1/2, -z+1/2, x)'), None
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'96i': (7, ('(x, y, z)', '(x, y+1/2, z+1/2)',
'(x+1/2, y, z+1/2)', '(x+1/2, y+1/2, z)',
'(-x, -y, z)', '(-x, -y+1/2, z+1/2)',
'(-x+1/2, -y, z+1/2)', '(-x+1/2, -y+1/2, z)',
'(-x, y, -z)', '(-x, y+1/2, -z+1/2)',
'(-x+1/2, y, -z+1/2)', '(-x+1/2, y+1/2, -z)',
'(x, -y, -z)', '(x, -y+1/2, -z+1/2)',
'(x+1/2, -y, -z+1/2)', '(x+1/2, -y+1/2, -z)',
'(z, x, y)', '(z, x+1/2, y+1/2)',
'(z+1/2, x, y+1/2)', '(z+1/2, x+1/2, y)',
'(z, -x, -y)', '(z, -x+1/2, -y+1/2)',
'(z+1/2, -x, -y+1/2)', '(z+1/2, -x+1/2, -y)',
'(-z, -x, y)', '(-z, -x+1/2, y+1/2)',
'(-z+1/2, -x, y+1/2)', '(-z+1/2, -x+1/2, y)',
'(-z, x, -y)', '(-z, x+1/2, -y+1/2)',
'(-z+1/2, x, -y+1/2)', '(-z+1/2, x+1/2, -y)',
'(y, z, x)', '(y, z+1/2, x+1/2)',
'(y+1/2, z, x+1/2)', '(y+1/2, z+1/2, x)',
'(-y, z, -x)', '(-y, z+1/2, -x+1/2)',
'(-y+1/2, z, -x+1/2)', '(-y+1/2, z+1/2, -x)',
'(y, -z, -x)', '(y, -z+1/2, -x+1/2)',
'(y+1/2, -z, -x+1/2)', '(y+1/2, -z+1/2, -x)',
'(-y, -z, x)', '(-y, -z+1/2, x+1/2)',
'(-y+1/2, -z, x+1/2)', '(-y+1/2, -z+1/2, x)',
'(y, x, z)', '(y, x+1/2, z+1/2)',
'(y+1/2, x, z+1/2)', '(y+1/2, x+1/2, z)',
'(-y, -x, z)', '(-y, -x+1/2, z+1/2)',
'(-y+1/2, -x, z+1/2)', '(-y+1/2, -x+1/2, z)',
'(y, -x, -z)', '(y, -x+1/2, -z+1/2)',
'(y+1/2, -x, -z+1/2)', '(y+1/2, -x+1/2, -z)',
'(-y, x, -z)', '(-y, x+1/2, -z+1/2)',
'(-y+1/2, x, -z+1/2)', '(-y+1/2, x+1/2, -z)',
'(x, z, y)', '(x, z+1/2, y+1/2)',
'(x+1/2, z, y+1/2)', '(x+1/2, z+1/2, y)',
'(-x, z, -y)', '(-x, z+1/2, -y+1/2)',
'(-x+1/2, z, -y+1/2)', '(-x+1/2, z+1/2, -y)',
'(-x, -z, y)', '(-x, -z+1/2, y+1/2)',
'(-x+1/2, -z, y+1/2)', '(-x+1/2, -z+1/2, y)',
'(x, -z, -y)', '(x, -z+1/2, -y+1/2)',
'(x+1/2, -z, -y+1/2)', '(x+1/2, -z+1/2, -y)',
'(z, y, x)', '(z, y+1/2, x+1/2)',
'(z+1/2, y, x+1/2)', '(z+1/2, y+1/2, x)',
'(z, -y, -x)', '(z, -y+1/2, -x+1/2)',
'(z+1/2, -y, -x+1/2)', '(z+1/2, -y+1/2, -x)',
'(-z, y, -x)', '(-z, y+1/2, -x+1/2)',
'(-z+1/2, y, -x+1/2)', '(-z+1/2, y+1/2, -x)',
'(-z, -y, x)', '(-z, -y+1/2, x+1/2)',
'(-z+1/2, -y, x+1/2)', '(-z+1/2, -y+1/2, x)'),
'hkl: h+k,h+l,k+l=2n, 0kl: k,l=2n, hhl: h+l=2n, '
'h00: h=2n')},
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'6b': (0, ('(0, 1/2, 1/2)', '(1/2, 0, 0)', '(1/2, 0, 1/2)',
'(0, 1/2, 0)', '(1/2, 1/2, 0)', '(0, 0, 1/2)'), None
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'8c': (1, ('(x, x, x)', '(x+1/2, x+1/2, x+1/2)', '(-x, -x, x)',
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'(-x+1/2, x+1/2, -x+1/2)', '(x, -x, -x)',
'(x+1/2, -x+1/2, -x+1/2)'), None),
'12d': (0, ('(1/4, 1/2, 0)', '(3/4, 0, 1/2)', '(3/4, 1/2, 0)',
'(1/4, 0, 1/2)', '(0, 1/4, 1/2)', '(1/2, 3/4, 0)',
'(0, 3/4, 1/2)', '(1/2, 1/4, 0)', '(1/2, 0, 1/4)',
'(0, 1/2, 3/4)', '(1/2, 0, 3/4)', '(0, 1/2, 1/4)'),
None),
'12e': (1, ('(x, 0, 0)', '(x+1/2, 1/2, 1/2)', '(-x, 0, 0)',
'(-x+1/2, 1/2, 1/2)', '(0, x, 0)',
'(1/2, x+1/2, 1/2)', '(0, -x, 0)',
'(1/2, -x+1/2, 1/2)', '(0, 0, x)',
'(1/2, 1/2, x+1/2)', '(0, 0, -x)',
'(1/2, 1/2, -x+1/2)'), None),
'24f': (1, ('(x, 1/2, 0)', '(x+1/2, 0, 1/2)', '(-x, 1/2, 0)',
'(-x+1/2, 0, 1/2)', '(0, x, 1/2)',
'(1/2, x+1/2, 0)', '(0, -x, 1/2)',
'(1/2, -x+1/2, 0)', '(1/2, 0, x)',
'(0, 1/2, x+1/2)', '(1/2, 0, -x)',
'(0, 1/2, -x+1/2)', '(1/2, x, 0)',
'(0, x+1/2, 1/2)', '(1/2, -x, 0)',
'(0, -x+1/2, 1/2)', '(x, 0, 1/2)',
'(x+1/2, 1/2, 0)', '(-x, 0, 1/2)',
'(-x+1/2, 1/2, 0)', '(0, 1/2, x)',
'(1/2, 0, x+1/2)', '(0, 1/2, -x)',
'(1/2, 0, -x+1/2)'), None),
'24g': (5, ('(x, x, z)', '(x+1/2, x+1/2, z+1/2)', '(-x, -x, z)',
'(-x+1/2, -x+1/2, z+1/2)', '(-x, x, -z)',
'(-x+1/2, x+1/2, -z+1/2)', '(x, -x, -z)',
'(x+1/2, -x+1/2, -z+1/2)', '(z, x, x)',
'(z+1/2, x+1/2, x+1/2)', '(z, -x, -x)',
'(z+1/2, -x+1/2, -x+1/2)', '(-z, -x, x)',
'(-z+1/2, -x+1/2, x+1/2)', '(-z, x, -x)',
'(-z+1/2, x+1/2, -x+1/2)', '(x, z, x)',
'(x+1/2, z+1/2, x+1/2)', '(-x, z, -x)',
'(-x+1/2, z+1/2, -x+1/2)', '(x, -z, -x)',
'(x+1/2, -z+1/2, -x+1/2)', '(-x, -z, x)',
'(-x+1/2, -z+1/2, x+1/2)'), None),
'48h': (7, ('(x, y, z)', '(x+1/2, y+1/2, z+1/2)', '(-x, -y, z)',
'(-x+1/2, -y+1/2, z+1/2)', '(-x, y, -z)',
'(-x+1/2, y+1/2, -z+1/2)', '(x, -y, -z)',
'(x+1/2, -y+1/2, -z+1/2)', '(z, x, y)',
'(z+1/2, x+1/2, y+1/2)', '(z, -x, -y)',
'(z+1/2, -x+1/2, -y+1/2)', '(-z, -x, y)',
'(-z+1/2, -x+1/2, y+1/2)', '(-z, x, -y)',
'(-z+1/2, x+1/2, -y+1/2)', '(y, z, x)',
'(y+1/2, z+1/2, x+1/2)', '(-y, z, -x)',
'(-y+1/2, z+1/2, -x+1/2)', '(y, -z, -x)',
'(y+1/2, -z+1/2, -x+1/2)', '(-y, -z, x)',
'(-y+1/2, -z+1/2, x+1/2)', '(y, x, z)',
'(y+1/2, x+1/2, z+1/2)', '(-y, -x, z)',
'(-y+1/2, -x+1/2, z+1/2)', '(y, -x, -z)',
'(y+1/2, -x+1/2, -z+1/2)', '(-y, x, -z)',
'(-y+1/2, x+1/2, -z+1/2)', '(x, z, y)',
'(x+1/2, z+1/2, y+1/2)', '(-x, z, -y)',
'(-x+1/2, z+1/2, -y+1/2)', '(-x, -z, y)',
'(-x+1/2, -z+1/2, y+1/2)', '(x, -z, -y)',
'(x+1/2, -z+1/2, -y+1/2)', '(z, y, x)',
'(z+1/2, y+1/2, x+1/2)', '(z, -y, -x)',
'(z+1/2, -y+1/2, -x+1/2)', '(-z, y, -x)',
'(-z+1/2, y+1/2, -x+1/2)', '(-z, -y, x)',
'(-z+1/2, -y+1/2, x+1/2)'),
'hkl: h+k+l=2n, 0kl: k+l=2n, hhl: l=2n, h00: h=2n')},
'218': {'2a': (0, ('(0, 0, 0)', '(1/2, 1/2, 1/2)'), 'hkl: h+k+l=2n'),
'6b': (0, ('(0, 1/2, 1/2)', '(1/2, 0, 1/2)', '(1/2, 1/2, 0)',
'(0, 1/2, 0)', '(1/2, 0, 0)', '(0, 0, 1/2)'),
'hkl: h+k+l=2n'),
'6c': (0, ('(1/4, 1/2, 0)', '(3/4, 1/2, 0)', '(0, 1/4, 1/2)',
'(0, 3/4, 1/2)', '(1/2, 0, 1/4)', '(1/2, 0, 3/4)'),
'hkl: h+k+l=2n or h=2n+1, k=4n, l=4n+2'),
'6d': (0, ('(1/4, 0, 1/2)', '(3/4, 0, 1/2)', '(1/2, 1/4, 0)',
'(1/2, 3/4, 0)', '(0, 1/2, 1/4)', '(0, 1/2, 3/4)'),
'hkl: h+k+l=2n or h=2n+1, k=4n, l=4n+2'),
'8e': (1, ('(x, x, x)', '(-x, -x, x)', '(-x, x, -x)',
'(x, -x, -x)', '(x+1/2, x+1/2, x+1/2)',
'(-x+1/2, -x+1/2, x+1/2)', '(x+1/2, -x+1/2, -x+1/2)',
'(-x+1/2, x+1/2, -x+1/2)'), 'hkl: h+k+l=2n'),
'12f': (1, ('(x, 0, 0)', '(-x, 0, 0)', '(0, x, 0)',
'(0, -x, 0)', '(0, 0, x)', '(0, 0, -x)',
'(1/2, x+1/2, 1/2)', '(1/2, -x+1/2, 1/2)',
'(x+1/2, 1/2, 1/2)', '(-x+1/2, 1/2, 1/2)',
'(1/2, 1/2, x+1/2)', '(1/2, 1/2, -x+1/2)'),
'hkl: h+k+l=2n'),
'12g': (1, ('(x, 1/2, 0)', '(-x, 1/2, 0)', '(0, x, 1/2)',
'(0, -x, 1/2)', '(1/2, 0, x)', '(1/2, 0, -x)',
'(0, x+1/2, 1/2)', '(0, -x+1/2, 1/2)',
'(x+1/2, 1/2, 0)', '(-x+1/2, 1/2, 0)',
'(1/2, 0, x+1/2)', '(1/2, 0, -x+1/2)'), 'hkl: h=2n'
),
'12h': (1, ('(x, 0, 1/2)', '(-x, 0, 1/2)', '(1/2, x, 0)',
'(1/2, -x, 0)', '(0, 1/2, x)', '(0, 1/2, -x)',
'(1/2, x+1/2, 0)', '(1/2, -x+1/2, 0)',
'(x+1/2, 0, 1/2)', '(-x+1/2, 0, 1/2)',
'(0, 1/2, x+1/2)', '(0, 1/2, -x+1/2)'), 'hkl: h=2n'
),
'24i': (7, ('(x, y, z)', '(-x, -y, z)', '(-x, y, -z)',
'(x, -y, -z)', '(z, x, y)', '(z, -x, -y)',
'(-z, -x, y)', '(-z, x, -y)', '(y, z, x)',
'(-y, z, -x)', '(y, -z, -x)', '(-y, -z, x)',
'(y+1/2, x+1/2, z+1/2)', '(-y+1/2, -x+1/2, z+1/2)',
'(y+1/2, -x+1/2, -z+1/2)',
'(-y+1/2, x+1/2, -z+1/2)', '(x+1/2, z+1/2, y+1/2)',
'(-x+1/2, z+1/2, -y+1/2)',
'(-x+1/2, -z+1/2, y+1/2)',
'(x+1/2, -z+1/2, -y+1/2)', '(z+1/2, y+1/2, x+1/2)',
'(z+1/2, -y+1/2, -x+1/2)',
'(-z+1/2, y+1/2, -x+1/2)',
'(-z+1/2, -y+1/2, x+1/2)'), 'hhl: l=2n, h00: h=2n'
)},
'219': {'8a': (0, ('(0, 0, 0)', '(0, 1/2, 1/2)', '(1/2, 0, 1/2)',
'(1/2, 1/2, 0)', '(1/2, 1/2, 1/2)', '(1/2, 0, 0)',
'(0, 1/2, 0)', '(0, 0, 1/2)'), 'hkl: h=2n'),
'8b': (0, ('(1/4, 1/4, 1/4)', '(1/4, 3/4, 3/4)',
'(3/4, 1/4, 3/4)', '(3/4, 3/4, 1/4)',
'(3/4, 3/4, 3/4)', '(3/4, 1/4, 1/4)',
'(1/4, 3/4, 1/4)', '(1/4, 1/4, 3/4)'), 'hkl: h=2n'),
'24c': (0, ('(0, 1/4, 1/4)', '(0, 3/4, 3/4)', '(1/2, 1/4, 3/4)',
'(1/2, 3/4, 1/4)', '(0, 3/4, 1/4)', '(0, 1/4, 3/4)',
'(1/2, 3/4, 3/4)', '(1/2, 1/4, 1/4)',
'(1/4, 0, 1/4)', '(1/4, 1/2, 3/4)', '(3/4, 0, 3/4)',
'(3/4, 1/2, 1/4)', '(1/4, 0, 3/4)',
'(1/4, 1/2, 1/4)', '(3/4, 0, 1/4)',
'(3/4, 1/2, 3/4)', '(1/4, 1/4, 0)',
'(1/4, 3/4, 1/2)', '(3/4, 1/4, 1/2)',
'(3/4, 3/4, 0)', '(3/4, 1/4, 0)', '(3/4, 3/4, 1/2)',
'(1/4, 1/4, 1/2)', '(1/4, 3/4, 0)'), 'hkl: h=2n'),
'24d': (0, ('(1/4, 0, 0)', '(1/4, 1/2, 1/2)', '(3/4, 0, 1/2)',
'(3/4, 1/2, 0)', '(3/4, 0, 0)', '(3/4, 1/2, 1/2)',
'(1/4, 0, 1/2)', '(1/4, 1/2, 0)', '(0, 1/4, 0)',
'(0, 3/4, 1/2)', '(1/2, 1/4, 1/2)', '(1/2, 3/4, 0)',
'(0, 3/4, 0)', '(0, 1/4, 1/2)', '(1/2, 3/4, 1/2)',
'(1/2, 1/4, 0)', '(0, 0, 1/4)', '(0, 1/2, 3/4)',
'(1/2, 0, 3/4)', '(1/2, 1/2, 1/4)', '(0, 0, 3/4)',
'(0, 1/2, 1/4)', '(1/2, 0, 1/4)', '(1/2, 1/2, 3/4)'
), 'hkl: h=2n'),
'32e': (1, ('(x, x, x)', '(x, x+1/2, x+1/2)',
'(x+1/2, x, x+1/2)', '(x+1/2, x+1/2, x)',
'(-x, -x, x)', '(-x, -x+1/2, x+1/2)',
'(-x+1/2, -x, x+1/2)', '(-x+1/2, -x+1/2, x)',
'(-x, x, -x)', '(-x, x+1/2, -x+1/2)',
'(-x+1/2, x, -x+1/2)', '(-x+1/2, x+1/2, -x)',
'(x, -x, -x)', '(x, -x+1/2, -x+1/2)',
'(x+1/2, -x, -x+1/2)', '(x+1/2, -x+1/2, -x)',
'(x+1/2, x+1/2, x+1/2)', '(x+1/2, x, x)',
'(x, x+1/2, x)', '(x, x, x+1/2)',
'(-x+1/2, -x+1/2, x+1/2)', '(-x+1/2, -x, x)',
'(-x, -x+1/2, x)', '(-x, -x, x+1/2)',
'(x+1/2, -x+1/2, -x+1/2)', '(x+1/2, -x, -x)',
'(x, -x+1/2, -x)', '(x, -x, -x+1/2)',
'(-x+1/2, x+1/2, -x+1/2)', '(-x+1/2, x, -x)',
'(-x, x+1/2, -x)', '(-x, x, -x+1/2)'), 'hkl: h=2n'),
'48f': (1, ('(x, 0, 0)', '(x, 1/2, 1/2)', '(x+1/2, 0, 1/2)',
'(x+1/2, 1/2, 0)', '(-x, 0, 0)', '(-x, 1/2, 1/2)',
'(-x+1/2, 0, 1/2)', '(-x+1/2, 1/2, 0)', '(0, x, 0)',
'(0, x+1/2, 1/2)', '(1/2, x, 1/2)',
'(1/2, x+1/2, 0)', '(0, -x, 0)', '(0, -x+1/2, 1/2)',
'(1/2, -x, 1/2)', '(1/2, -x+1/2, 0)', '(0, 0, x)',
'(0, 1/2, x+1/2)', '(1/2, 0, x+1/2)',
'(1/2, 1/2, x)', '(0, 0, -x)', '(0, 1/2, -x+1/2)',
'(1/2, 0, -x+1/2)', '(1/2, 1/2, -x)',
'(1/2, x+1/2, 1/2)', '(1/2, x, 0)', '(0, x+1/2, 0)',
'(0, x, 1/2)', '(1/2, -x+1/2, 1/2)', '(1/2, -x, 0)',
'(0, -x+1/2, 0)', '(0, -x, 1/2)',
'(x+1/2, 1/2, 1/2)', '(x+1/2, 0, 0)', '(x, 1/2, 0)',
'(x, 0, 1/2)', '(-x+1/2, 1/2, 1/2)',
'(-x+1/2, 0, 0)', '(-x, 1/2, 0)', '(-x, 0, 1/2)',
'(1/2, 1/2, x+1/2)', '(1/2, 0, x)', '(0, 1/2, x)',
'(0, 0, x+1/2)', '(1/2, 1/2, -x+1/2)',
'(1/2, 0, -x)', '(0, 1/2, -x)', '(0, 0, -x+1/2)'),
'hkl: h=2n'),
'48g': (1, ('(x, 1/4, 1/4)', '(x, 3/4, 3/4)',
'(x+1/2, 1/4, 3/4)', '(x+1/2, 3/4, 1/4)',
'(-x, 3/4, 1/4)', '(-x, 1/4, 3/4)',
'(-x+1/2, 3/4, 3/4)', '(-x+1/2, 1/4, 1/4)',
'(1/4, x, 1/4)', '(1/4, x+1/2, 3/4)',
'(3/4, x, 3/4)', '(3/4, x+1/2, 1/4)',
'(1/4, -x, 3/4)', '(1/4, -x+1/2, 1/4)',
'(3/4, -x, 1/4)', '(3/4, -x+1/2, 3/4)',
'(1/4, 1/4, x)', '(1/4, 3/4, x+1/2)',
'(3/4, 1/4, x+1/2)', '(3/4, 3/4, x)',
'(3/4, 1/4, -x)', '(3/4, 3/4, -x+1/2)',
'(1/4, 1/4, -x+1/2)', '(1/4, 3/4, -x)',
'(3/4, x+1/2, 3/4)', '(3/4, x, 1/4)',
'(1/4, x+1/2, 1/4)', '(1/4, x, 3/4)',
'(1/4, -x+1/2, 3/4)', '(1/4, -x, 1/4)',
'(3/4, -x+1/2, 1/4)', '(3/4, -x, 3/4)',
'(x+1/2, 3/4, 3/4)', '(x+1/2, 1/4, 1/4)',
'(x, 3/4, 1/4)', '(x, 1/4, 3/4)',
'(-x+1/2, 3/4, 1/4)', '(-x+1/2, 1/4, 3/4)',
'(-x, 3/4, 3/4)', '(-x, 1/4, 1/4)',
'(3/4, 3/4, x+1/2)', '(3/4, 1/4, x)',
'(1/4, 3/4, x)', '(1/4, 1/4, x+1/2)',
'(3/4, 1/4, -x+1/2)', '(3/4, 3/4, -x)',
'(1/4, 1/4, -x)', '(1/4, 3/4, -x+1/2)'), 'hkl: h=2n'
),
'96h': (7, ('(x, y, z)', '(x, y+1/2, z+1/2)',
'(x+1/2, y, z+1/2)', '(x+1/2, y+1/2, z)',
'(-x, -y, z)', '(-x, -y+1/2, z+1/2)',
'(-x+1/2, -y, z+1/2)', '(-x+1/2, -y+1/2, z)',
'(-x, y, -z)', '(-x, y+1/2, -z+1/2)',
'(-x+1/2, y, -z+1/2)', '(-x+1/2, y+1/2, -z)',
'(x, -y, -z)', '(x, -y+1/2, -z+1/2)',
'(x+1/2, -y, -z+1/2)', '(x+1/2, -y+1/2, -z)',
'(z, x, y)', '(z, x+1/2, y+1/2)',
'(z+1/2, x, y+1/2)', '(z+1/2, x+1/2, y)',
'(z, -x, -y)', '(z, -x+1/2, -y+1/2)',
'(z+1/2, -x, -y+1/2)', '(z+1/2, -x+1/2, -y)',
'(-z, -x, y)', '(-z, -x+1/2, y+1/2)',
'(-z+1/2, -x, y+1/2)', '(-z+1/2, -x+1/2, y)',
'(-z, x, -y)', '(-z, x+1/2, -y+1/2)',
'(-z+1/2, x, -y+1/2)', '(-z+1/2, x+1/2, -y)',
'(y, z, x)', '(y, z+1/2, x+1/2)',
'(y+1/2, z, x+1/2)', '(y+1/2, z+1/2, x)',
'(-y, z, -x)', '(-y, z+1/2, -x+1/2)',
'(-y+1/2, z, -x+1/2)', '(-y+1/2, z+1/2, -x)',
'(y, -z, -x)', '(y, -z+1/2, -x+1/2)',
'(y+1/2, -z, -x+1/2)', '(y+1/2, -z+1/2, -x)',
'(-y, -z, x)', '(-y, -z+1/2, x+1/2)',
'(-y+1/2, -z, x+1/2)', '(-y+1/2, -z+1/2, x)',
'(y+1/2, x+1/2, z+1/2)', '(y+1/2, x, z)',
'(y, x+1/2, z)', '(y, x, z+1/2)',
'(-y+1/2, -x+1/2, z+1/2)', '(-y+1/2, -x, z)',
'(-y, -x+1/2, z)', '(-y, -x, z+1/2)',
'(y+1/2, -x+1/2, -z+1/2)', '(y+1/2, -x, -z)',
'(y, -x+1/2, -z)', '(y, -x, -z+1/2)',
'(-y+1/2, x+1/2, -z+1/2)', '(-y+1/2, x, -z)',
'(-y, x+1/2, -z)', '(-y, x, -z+1/2)',
'(x+1/2, z+1/2, y+1/2)', '(x+1/2, z, y)',
'(x, z+1/2, y)', '(x, z, y+1/2)',
'(-x+1/2, z+1/2, -y+1/2)', '(-x+1/2, z, -y)',
'(-x, z+1/2, -y)', '(-x, z, -y+1/2)',
'(-x+1/2, -z+1/2, y+1/2)', '(-x+1/2, -z, y)',
'(-x, -z+1/2, y)', '(-x, -z, y+1/2)',
'(x+1/2, -z+1/2, -y+1/2)', '(x+1/2, -z, -y)',
'(x, -z+1/2, -y)', '(x, -z, -y+1/2)',
'(z+1/2, y+1/2, x+1/2)', '(z+1/2, y, x)',
'(z, y+1/2, x)', '(z, y, x+1/2)',
'(z+1/2, -y+1/2, -x+1/2)', '(z+1/2, -y, -x)',
'(z, -y+1/2, -x)', '(z, -y, -x+1/2)',
'(-z+1/2, y+1/2, -x+1/2)', '(-z+1/2, y, -x)',
'(-z, y+1/2, -x)', '(-z, y, -x+1/2)',
'(-z+1/2, -y+1/2, x+1/2)', '(-z+1/2, -y, x)',
'(-z, -y+1/2, x)', '(-z, -y, x+1/2)'),
'hkl: h+k=2n, h+l,k+l=2n, 0kl: k,l=2n, hhl: h,l=2n, '
'h00: h=2n')},
'220': {'12a': (0, ('(3/8, 0, 1/4)', '(7/8, 1/2, 3/4)', '(1/8, 0, 3/4)',
'(5/8, 1/2, 1/4)', '(1/4, 3/8, 0)',
'(3/4, 7/8, 1/2)', '(3/4, 1/8, 0)',
'(1/4, 5/8, 1/2)', '(0, 1/4, 3/8)',
'(1/2, 3/4, 7/8)', '(0, 3/4, 1/8)',
'(1/2, 1/4, 5/8)'),
'hkl: h,k=2n, h+k+l=4n or h,k=2n+1, '
'l=4n+2 or h=8n, k=8n+4, h+k+l=4n+2 or h=8n+1, '
'k=8n+3, l=4n or h=8n+1, k=8n+5, l=4n or h=8n+7, '
'k=8n+3, l=4n or h=8n+7, k=8n+5, l=4n'),
'12b': (0, ('(7/8, 0, 1/4)', '(3/8, 1/2, 3/4)', '(5/8, 0, 3/4)',
'(1/8, 1/2, 1/4)', '(1/4, 7/8, 0)',
'(3/4, 3/8, 1/2)', '(3/4, 5/8, 0)',
'(1/4, 1/8, 1/2)', '(0, 1/4, 7/8)',
'(1/2, 3/4, 3/8)', '(0, 3/4, 5/8)',
'(1/2, 1/4, 1/8)'),
'hkl: h,k=2n, h+k+l=4n or h,k=2n+1, '
'l=4n+2 or h=8n, k=8n+4, h+k+l=4n+2 or h=8n+1, '
'k=8n+3, l=4n or h=8n+1, k=8n+5, l=4n or h=8n+7, '
'k=8n+3, l=4n or h=8n+7, k=8n+5, l=4n'),
'16c': (1, ('(x, x, x)', '(x+1/2, x+1/2, x+1/2)',
'(-x+1/2, -x, x+1/2)', '(-x, -x+1/2, x)',
'(-x, x+1/2, -x+1/2)', '(-x+1/2, x, -x)',
'(x+1/2, -x+1/2, -x)', '(x, -x, -x+1/2)',
'(x+1/4, x+1/4, x+1/4)', '(x+3/4, x+3/4, x+3/4)',
'(-x+1/4, -x+3/4, x+3/4)',
'(-x+3/4, -x+1/4, x+1/4)',
'(x+3/4, -x+1/4, -x+3/4)',
'(x+1/4, -x+3/4, -x+1/4)',
'(-x+3/4, x+3/4, -x+1/4)',
'(-x+1/4, x+1/4, -x+3/4)'), 'hkl: h=2n+1 or h+k+l=4n'
),
'24d': (1, ('(x, 0, 1/4)', '(x+1/2, 1/2, 3/4)',
'(-x+1/2, 0, 3/4)', '(-x, 1/2, 1/4)', '(1/4, x, 0)',
'(3/4, x+1/2, 1/2)', '(3/4, -x+1/2, 0)',
'(1/4, -x, 1/2)', '(0, 1/4, x)',
'(1/2, 3/4, x+1/2)', '(0, 3/4, -x+1/2)',
'(1/2, 1/4, -x)', '(1/4, x+1/4, 1/2)',
'(3/4, x+3/4, 0)', '(1/4, -x+3/4, 0)',
'(3/4, -x+1/4, 1/2)', '(x+1/4, 1/2, 1/4)',
'(x+3/4, 0, 3/4)', '(-x+3/4, 0, 1/4)',
'(-x+1/4, 1/2, 3/4)', '(1/2, 1/4, x+1/4)',
'(0, 3/4, x+3/4)', '(0, 1/4, -x+3/4)',
'(1/2, 3/4, -x+1/4)'), 'hkl: h=2n+1 or h=4n'),
'48e': (7, ('(x, y, z)', '(x+1/2, y+1/2, z+1/2)',
'(-x+1/2, -y, z+1/2)', '(-x, -y+1/2, z)',
'(-x, y+1/2, -z+1/2)', '(-x+1/2, y, -z)',
'(x+1/2, -y+1/2, -z)', '(x, -y, -z+1/2)',
'(z, x, y)', '(z+1/2, x+1/2, y+1/2)',
'(z+1/2, -x+1/2, -y)', '(z, -x, -y+1/2)',
'(-z+1/2, -x, y+1/2)', '(-z, -x+1/2, y)',
'(-z, x+1/2, -y+1/2)', '(-z+1/2, x, -y)',
'(y, z, x)', '(y+1/2, z+1/2, x+1/2)',
'(-y, z+1/2, -x+1/2)', '(-y+1/2, z, -x)',
'(y+1/2, -z+1/2, -x)', '(y, -z, -x+1/2)',
'(-y+1/2, -z, x+1/2)', '(-y, -z+1/2, x)',
'(y+1/4, x+1/4, z+1/4)', '(y+3/4, x+3/4, z+3/4)',
'(-y+1/4, -x+3/4, z+3/4)',
'(-y+3/4, -x+1/4, z+1/4)',
'(y+3/4, -x+1/4, -z+3/4)',
'(y+1/4, -x+3/4, -z+1/4)',
'(-y+3/4, x+3/4, -z+1/4)',
'(-y+1/4, x+1/4, -z+3/4)', '(x+1/4, z+1/4, y+1/4)',
'(x+3/4, z+3/4, y+3/4)', '(-x+3/4, z+3/4, -y+1/4)',
'(-x+1/4, z+1/4, -y+3/4)',
'(-x+1/4, -z+3/4, y+3/4)',
'(-x+3/4, -z+1/4, y+1/4)',
'(x+3/4, -z+1/4, -y+3/4)',
'(x+1/4, -z+3/4, -y+1/4)', '(z+1/4, y+1/4, x+1/4)',
'(z+3/4, y+3/4, x+3/4)', '(z+3/4, -y+1/4, -x+3/4)',
'(z+1/4, -y+3/4, -x+1/4)',
'(-z+3/4, y+3/4, -x+1/4)',
'(-z+1/4, y+1/4, -x+3/4)',
'(-z+1/4, -y+3/4, x+3/4)',
'(-z+3/4, -y+1/4, x+1/4)'),
'hkl: h+k+l=2n, 0kl: k+l=2n, hhl: 2h+l=4n, h00: h=4n')},
'221': {'1a': (0, ('(0, 0, 0)', ), None),
'1b': (0, ('(1/2, 1/2, 1/2)', ), None),
'3c': (0, ('(0, 1/2, 1/2)', '(1/2, 0, 1/2)', '(1/2, 1/2, 0)'),
None),
'3d': (0, ('(1/2, 0, 0)', '(0, 1/2, 0)', '(0, 0, 1/2)'), None),
'6e': (1, ('(x, 0, 0)', '(-x, 0, 0)', '(0, x, 0)', '(0, -x, 0)',
'(0, 0, x)', '(0, 0, -x)'), None),
'6f': (1, ('(x, 1/2, 1/2)', '(-x, 1/2, 1/2)', '(1/2, x, 1/2)',
'(1/2, -x, 1/2)', '(1/2, 1/2, x)', '(1/2, 1/2, -x)'),
None),
'8g': (1, ('(x, x, x)', '(-x, -x, x)', '(-x, x, -x)',
'(x, -x, -x)', '(x, x, -x)', '(-x, -x, -x)',
'(x, -x, x)', '(-x, x, x)'), None),
'12h': (1, ('(x, 1/2, 0)', '(-x, 1/2, 0)', '(0, x, 1/2)',
'(0, -x, 1/2)', '(1/2, 0, x)', '(1/2, 0, -x)',
'(1/2, x, 0)', '(1/2, -x, 0)', '(x, 0, 1/2)',
'(-x, 0, 1/2)', '(0, 1/2, -x)', '(0, 1/2, x)'), None
),
'12i': (2, ('(0, y, y)', '(0, -y, y)', '(0, y, -y)',
'(0, -y, -y)', '(y, 0, y)', '(y, 0, -y)',
'(-y, 0, y)', '(-y, 0, -y)', '(y, y, 0)',
'(-y, y, 0)', '(y, -y, 0)', '(-y, -y, 0)'), None),
'12j': (2, ('(1/2, y, y)', '(1/2, -y, y)', '(1/2, y, -y)',
'(1/2, -y, -y)', '(y, 1/2, y)', '(y, 1/2, -y)',
'(-y, 1/2, y)', '(-y, 1/2, -y)', '(y, y, 1/2)',
'(-y, y, 1/2)', '(y, -y, 1/2)', '(-y, -y, 1/2)'),
None),
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'(z+1/2, -y+1/2, -x+1/2)', '(z+1/2, y+1/2, x+1/2)'),
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'(-y+1/2, y, 3/4)', '(y+1/2, y, 1/4)'), None),
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'(-y, y, 1/2)', '(y+1/2, y, 0)',
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'(-z+1/2, -y+1/2, x)', '(-z+1/2, y, -x+1/2)',
'(z, -y+1/2, -x+1/2)', '(z, y, x)'), 'n/a')},
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'(3/4, 1/2, 1/4)', '(1/4, 0, 3/4)',
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'(x+1/2, x, -x+1/2)', '(x+1/2, x+1/2, -x)',
'(-x, -x, -x)', '(-x, -x+1/2, -x+1/2)',
'(-x+1/2, -x, -x+1/2)', '(-x+1/2, -x+1/2, -x)',
'(x, -x, x)', '(x, -x+1/2, x+1/2)',
'(x+1/2, -x, x+1/2)', '(x+1/2, -x+1/2, x)',
'(-x, x, x)', '(-x, x+1/2, x+1/2)',
'(-x+1/2, x, x+1/2)', '(-x+1/2, x+1/2, x)'), None),
'48g': (1, ('(x, 1/4, 1/4)', '(x, 3/4, 3/4)',
'(x+1/2, 1/4, 3/4)', '(x+1/2, 3/4, 1/4)',
'(-x, 3/4, 1/4)', '(-x, 1/4, 3/4)',
'(-x+1/2, 3/4, 3/4)', '(-x+1/2, 1/4, 1/4)',
'(1/4, x, 1/4)', '(1/4, x+1/2, 3/4)',
'(3/4, x, 3/4)', '(3/4, x+1/2, 1/4)',
'(1/4, -x, 3/4)', '(1/4, -x+1/2, 1/4)',
'(3/4, -x, 1/4)', '(3/4, -x+1/2, 3/4)',
'(1/4, 1/4, x)', '(1/4, 3/4, x+1/2)',
'(3/4, 1/4, x+1/2)', '(3/4, 3/4, x)',
'(3/4, 1/4, -x)', '(3/4, 3/4, -x+1/2)',
'(1/4, 1/4, -x+1/2)', '(1/4, 3/4, -x)',
'(1/4, x, 3/4)', '(1/4, x+1/2, 1/4)',
'(3/4, x, 1/4)', '(3/4, x+1/2, 3/4)',
'(3/4, -x, 3/4)', '(3/4, -x+1/2, 1/4)',
'(1/4, -x, 1/4)', '(1/4, -x+1/2, 3/4)',
'(x, 1/4, 3/4)', '(x, 3/4, 1/4)',
'(x+1/2, 1/4, 1/4)', '(x+1/2, 3/4, 3/4)',
'(-x, 1/4, 1/4)', '(-x, 3/4, 3/4)',
'(-x+1/2, 1/4, 3/4)', '(-x+1/2, 3/4, 1/4)',
'(1/4, 1/4, -x)', '(1/4, 3/4, -x+1/2)',
'(3/4, 1/4, -x+1/2)', '(3/4, 3/4, -x)',
'(1/4, 3/4, x)', '(1/4, 1/4, x+1/2)',
'(3/4, 3/4, x+1/2)', '(3/4, 1/4, x)'), 'hkl: h=2n'),
'48h': (2, ('(0, y, y)', '(0, y+1/2, y+1/2)', '(1/2, y, y+1/2)',
'(1/2, y+1/2, y)', '(0, -y, y)',
'(0, -y+1/2, y+1/2)', '(1/2, -y, y+1/2)',
'(1/2, -y+1/2, y)', '(0, y, -y)',
'(0, y+1/2, -y+1/2)', '(1/2, y, -y+1/2)',
'(1/2, y+1/2, -y)', '(0, -y, -y)',
'(0, -y+1/2, -y+1/2)', '(1/2, -y, -y+1/2)',
'(1/2, -y+1/2, -y)', '(y, 0, y)', '(y, 1/2, y+1/2)',
'(y+1/2, 0, y+1/2)', '(y+1/2, 1/2, y)',
'(y, 0, -y)', '(y, 1/2, -y+1/2)',
'(y+1/2, 0, -y+1/2)', '(y+1/2, 1/2, -y)',
'(-y, 0, y)', '(-y, 1/2, y+1/2)',
'(-y+1/2, 0, y+1/2)', '(-y+1/2, 1/2, y)',
'(-y, 0, -y)', '(-y, 1/2, -y+1/2)',
'(-y+1/2, 0, -y+1/2)', '(-y+1/2, 1/2, -y)',
'(y, y, 0)', '(y, y+1/2, 1/2)', '(y+1/2, y, 1/2)',
'(y+1/2, y+1/2, 0)', '(-y, y, 0)',
'(-y, y+1/2, 1/2)', '(-y+1/2, y, 1/2)',
'(-y+1/2, y+1/2, 0)', '(y, -y, 0)',
'(y, -y+1/2, 1/2)', '(y+1/2, -y, 1/2)',
'(y+1/2, -y+1/2, 0)', '(-y, -y, 0)',
'(-y, -y+1/2, 1/2)', '(-y+1/2, -y, 1/2)',
'(-y+1/2, -y+1/2, 0)'), None),
'48i': (2, ('(1/2, y, y)', '(1/2, y+1/2, y+1/2)',
'(0, y, y+1/2)', '(0, y+1/2, y)', '(1/2, -y, y)',
'(1/2, -y+1/2, y+1/2)', '(0, -y, y+1/2)',
'(0, -y+1/2, y)', '(1/2, y, -y)',
'(1/2, y+1/2, -y+1/2)', '(0, y, -y+1/2)',
'(0, y+1/2, -y)', '(1/2, -y, -y)',
'(1/2, -y+1/2, -y+1/2)', '(0, -y, -y+1/2)',
'(0, -y+1/2, -y)', '(y, 1/2, y)', '(y, 0, y+1/2)',
'(y+1/2, 1/2, y+1/2)', '(y+1/2, 0, y)',
'(y, 1/2, -y)', '(y, 0, -y+1/2)',
'(y+1/2, 1/2, -y+1/2)', '(y+1/2, 0, -y)',
'(-y, 1/2, y)', '(-y, 0, y+1/2)',
'(-y+1/2, 1/2, y+1/2)', '(-y+1/2, 0, y)',
'(-y, 1/2, -y)', '(-y, 0, -y+1/2)',
'(-y+1/2, 1/2, -y+1/2)', '(-y+1/2, 0, -y)',
'(y, y, 1/2)', '(y, y+1/2, 0)', '(y+1/2, y, 0)',
'(y+1/2, y+1/2, 1/2)', '(-y, y, 1/2)',
'(-y, y+1/2, 0)', '(-y+1/2, y, 0)',
'(-y+1/2, y+1/2, 1/2)', '(y, -y, 1/2)',
'(y, -y+1/2, 0)', '(y+1/2, -y, 0)',
'(y+1/2, -y+1/2, 1/2)', '(-y, -y, 1/2)',
'(-y, -y+1/2, 0)', '(-y+1/2, -y, 0)',
'(-y+1/2, -y+1/2, 1/2)'), None),
'96j': (6, ('(0, y, z)', '(0, y+1/2, z+1/2)', '(1/2, y, z+1/2)',
'(1/2, y+1/2, z)', '(0, -y, z)',
'(0, -y+1/2, z+1/2)', '(1/2, -y, z+1/2)',
'(1/2, -y+1/2, z)', '(0, y, -z)',
'(0, y+1/2, -z+1/2)', '(1/2, y, -z+1/2)',
'(1/2, y+1/2, -z)', '(0, -y, -z)',
'(0, -y+1/2, -z+1/2)', '(1/2, -y, -z+1/2)',
'(1/2, -y+1/2, -z)', '(z, 0, y)', '(z, 1/2, y+1/2)',
'(z+1/2, 0, y+1/2)', '(z+1/2, 1/2, y)',
'(z, 0, -y)', '(z, 1/2, -y+1/2)',
'(z+1/2, 0, -y+1/2)', '(z+1/2, 1/2, -y)',
'(-z, 0, y)', '(-z, 1/2, y+1/2)',
'(-z+1/2, 0, y+1/2)', '(-z+1/2, 1/2, y)',
'(-z, 0, -y)', '(-z, 1/2, -y+1/2)',
'(-z+1/2, 0, -y+1/2)', '(-z+1/2, 1/2, -y)',
'(y, z, 0)', '(y, z+1/2, 1/2)', '(y+1/2, z, 1/2)',
'(y+1/2, z+1/2, 0)', '(-y, z, 0)',
'(-y, z+1/2, 1/2)', '(-y+1/2, z, 1/2)',
'(-y+1/2, z+1/2, 0)', '(y, -z, 0)',
'(y, -z+1/2, 1/2)', '(y+1/2, -z, 1/2)',
'(y+1/2, -z+1/2, 0)', '(-y, -z, 0)',
'(-y, -z+1/2, 1/2)', '(-y+1/2, -z, 1/2)',
'(-y+1/2, -z+1/2, 0)', '(y, 0, -z)',
'(y, 1/2, -z+1/2)', '(y+1/2, 0, -z+1/2)',
'(y+1/2, 1/2, -z)', '(-y, 0, -z)',
'(-y, 1/2, -z+1/2)', '(-y+1/2, 0, -z+1/2)',
'(-y+1/2, 1/2, -z)', '(y, 0, z)', '(y, 1/2, z+1/2)',
'(y+1/2, 0, z+1/2)', '(y+1/2, 1/2, z)',
'(-y, 0, z)', '(-y, 1/2, z+1/2)',
'(-y+1/2, 0, z+1/2)', '(-y+1/2, 1/2, z)',
'(0, z, -y)', '(0, z+1/2, -y+1/2)',
'(1/2, z, -y+1/2)', '(1/2, z+1/2, -y)', '(0, z, y)',
'(0, z+1/2, y+1/2)', '(1/2, z, y+1/2)',
'(1/2, z+1/2, y)', '(0, -z, -y)',
'(0, -z+1/2, -y+1/2)', '(1/2, -z, -y+1/2)',
'(1/2, -z+1/2, -y)', '(0, -z, y)',
'(0, -z+1/2, y+1/2)', '(1/2, -z, y+1/2)',
'(1/2, -z+1/2, y)', '(z, y, 0)', '(z, y+1/2, 1/2)',
'(z+1/2, y, 1/2)', '(z+1/2, y+1/2, 0)',
'(z, -y, 0)', '(z, -y+1/2, 1/2)',
'(z+1/2, -y, 1/2)', '(z+1/2, -y+1/2, 0)',
'(-z, y, 0)', '(-z, y+1/2, 1/2)',
'(-z+1/2, y, 1/2)', '(-z+1/2, y+1/2, 0)',
'(-z, -y, 0)', '(-z, -y+1/2, 1/2)',
'(-z+1/2, -y, 1/2)', '(-z+1/2, -y+1/2, 0)'), None),
'96k': (5, ('(x, x, z)', '(x, x+1/2, z+1/2)',
'(x+1/2, x, z+1/2)', '(x+1/2, x+1/2, z)',
'(-x, -x, z)', '(-x, -x+1/2, z+1/2)',
'(-x+1/2, -x, z+1/2)', '(-x+1/2, -x+1/2, z)',
'(-x, x, -z)', '(-x, x+1/2, -z+1/2)',
'(-x+1/2, x, -z+1/2)', '(-x+1/2, x+1/2, -z)',
'(x, -x, -z)', '(x, -x+1/2, -z+1/2)',
'(x+1/2, -x, -z+1/2)', '(x+1/2, -x+1/2, -z)',
'(z, x, x)', '(z, x+1/2, x+1/2)',
'(z+1/2, x, x+1/2)', '(z+1/2, x+1/2, x)',
'(z, -x, -x)', '(z, -x+1/2, -x+1/2)',
'(z+1/2, -x, -x+1/2)', '(z+1/2, -x+1/2, -x)',
'(-z, -x, x)', '(-z, -x+1/2, x+1/2)',
'(-z+1/2, -x, x+1/2)', '(-z+1/2, -x+1/2, x)',
'(-z, x, -x)', '(-z, x+1/2, -x+1/2)',
'(-z+1/2, x, -x+1/2)', '(-z+1/2, x+1/2, -x)',
'(x, z, x)', '(x, z+1/2, x+1/2)',
'(x+1/2, z, x+1/2)', '(x+1/2, z+1/2, x)',
'(-x, z, -x)', '(-x, z+1/2, -x+1/2)',
'(-x+1/2, z, -x+1/2)', '(-x+1/2, z+1/2, -x)',
'(x, -z, -x)', '(x, -z+1/2, -x+1/2)',
'(x+1/2, -z, -x+1/2)', '(x+1/2, -z+1/2, -x)',
'(-x, -z, x)', '(-x, -z+1/2, x+1/2)',
'(-x+1/2, -z, x+1/2)', '(-x+1/2, -z+1/2, x)',
'(x, x, -z)', '(x, x+1/2, -z+1/2)',
'(x+1/2, x, -z+1/2)', '(x+1/2, x+1/2, -z)',
'(-x, -x, -z)', '(-x, -x+1/2, -z+1/2)',
'(-x+1/2, -x, -z+1/2)', '(-x+1/2, -x+1/2, -z)',
'(x, -x, z)', '(x, -x+1/2, z+1/2)',
'(x+1/2, -x, z+1/2)', '(x+1/2, -x+1/2, z)',
'(-x, x, z)', '(-x, x+1/2, z+1/2)',
'(-x+1/2, x, z+1/2)', '(-x+1/2, x+1/2, z)',
'(x, z, -x)', '(x, z+1/2, -x+1/2)',
'(x+1/2, z, -x+1/2)', '(x+1/2, z+1/2, -x)',
'(-x, z, x)', '(-x, z+1/2, x+1/2)',
'(-x+1/2, z, x+1/2)', '(-x+1/2, z+1/2, x)',
'(-x, -z, -x)', '(-x, -z+1/2, -x+1/2)',
'(-x+1/2, -z, -x+1/2)', '(-x+1/2, -z+1/2, -x)',
'(x, -z, x)', '(x, -z+1/2, x+1/2)',
'(x+1/2, -z, x+1/2)', '(x+1/2, -z+1/2, x)',
'(z, x, -x)', '(z, x+1/2, -x+1/2)',
'(z+1/2, x, -x+1/2)', '(z+1/2, x+1/2, -x)',
'(z, -x, x)', '(z, -x+1/2, x+1/2)',
'(z+1/2, -x, x+1/2)', '(z+1/2, -x+1/2, x)',
'(-z, x, x)', '(-z, x+1/2, x+1/2)',
'(-z+1/2, x, x+1/2)', '(-z+1/2, x+1/2, x)',
'(-z, -x, -x)', '(-z, -x+1/2, -x+1/2)',
'(-z+1/2, -x, -x+1/2)', '(-z+1/2, -x+1/2, -x)'), None
),
'192l': (7, ('(x, y, z)', '(x, y+1/2, z+1/2)',
'(x+1/2, y, z+1/2)', '(x+1/2, y+1/2, z)',
'(-x, -y, z)', '(-x, -y+1/2, z+1/2)',
'(-x+1/2, -y, z+1/2)', '(-x+1/2, -y+1/2, z)',
'(-x, y, -z)', '(-x, y+1/2, -z+1/2)',
'(-x+1/2, y, -z+1/2)', '(-x+1/2, y+1/2, -z)',
'(x, -y, -z)', '(x, -y+1/2, -z+1/2)',
'(x+1/2, -y, -z+1/2)', '(x+1/2, -y+1/2, -z)',
'(z, x, y)', '(z, x+1/2, y+1/2)',
'(z+1/2, x, y+1/2)', '(z+1/2, x+1/2, y)',
'(z, -x, -y)', '(z, -x+1/2, -y+1/2)',
'(z+1/2, -x, -y+1/2)', '(z+1/2, -x+1/2, -y)',
'(-z, -x, y)', '(-z, -x+1/2, y+1/2)',
'(-z+1/2, -x, y+1/2)', '(-z+1/2, -x+1/2, y)',
'(-z, x, -y)', '(-z, x+1/2, -y+1/2)',
'(-z+1/2, x, -y+1/2)', '(-z+1/2, x+1/2, -y)',
'(y, z, x)', '(y, z+1/2, x+1/2)',
'(y+1/2, z, x+1/2)', '(y+1/2, z+1/2, x)',
'(-y, z, -x)', '(-y, z+1/2, -x+1/2)',
'(-y+1/2, z, -x+1/2)', '(-y+1/2, z+1/2, -x)',
'(y, -z, -x)', '(y, -z+1/2, -x+1/2)',
'(y+1/2, -z, -x+1/2)', '(y+1/2, -z+1/2, -x)',
'(-y, -z, x)', '(-y, -z+1/2, x+1/2)',
'(-y+1/2, -z, x+1/2)', '(-y+1/2, -z+1/2, x)',
'(y, x, -z)', '(y, x+1/2, -z+1/2)',
'(y+1/2, x, -z+1/2)', '(y+1/2, x+1/2, -z)',
'(-y, -x, -z)', '(-y, -x+1/2, -z+1/2)',
'(-y+1/2, -x, -z+1/2)', '(-y+1/2, -x+1/2, -z)',
'(y, -x, z)', '(y, -x+1/2, z+1/2)',
'(y+1/2, -x, z+1/2)', '(y+1/2, -x+1/2, z)',
'(-y, x, z)', '(-y, x+1/2, z+1/2)',
'(-y+1/2, x, z+1/2)', '(-y+1/2, x+1/2, z)',
'(x, z, -y)', '(x, z+1/2, -y+1/2)',
'(x+1/2, z, -y+1/2)', '(x+1/2, z+1/2, -y)',
'(-x, z, y)', '(-x, z+1/2, y+1/2)',
'(-x+1/2, z, y+1/2)', '(-x+1/2, z+1/2, y)',
'(-x, -z, -y)', '(-x, -z+1/2, -y+1/2)',
'(-x+1/2, -z, -y+1/2)', '(-x+1/2, -z+1/2, -y)',
'(x, -z, y)', '(x, -z+1/2, y+1/2)',
'(x+1/2, -z, y+1/2)', '(x+1/2, -z+1/2, y)',
'(z, y, -x)', '(z, y+1/2, -x+1/2)',
'(z+1/2, y, -x+1/2)', '(z+1/2, y+1/2, -x)',
'(z, -y, x)', '(z, -y+1/2, x+1/2)',
'(z+1/2, -y, x+1/2)', '(z+1/2, -y+1/2, x)',
'(-z, y, x)', '(-z, y+1/2, x+1/2)',
'(-z+1/2, y, x+1/2)', '(-z+1/2, y+1/2, x)',
'(-z, -y, -x)', '(-z, -y+1/2, -x+1/2)',
'(-z+1/2, -y, -x+1/2)', '(-z+1/2, -y+1/2, -x)',
'(-x, -y, -z)', '(-x, -y+1/2, -z+1/2)',
'(-x+1/2, -y, -z+1/2)', '(-x+1/2, -y+1/2, -z)',
'(x, y, -z)', '(x, y+1/2, -z+1/2)',
'(x+1/2, y, -z+1/2)', '(x+1/2, y+1/2, -z)',
'(x, -y, z)', '(x, -y+1/2, z+1/2)',
'(x+1/2, -y, z+1/2)', '(x+1/2, -y+1/2, z)',
'(-x, y, z)', '(-x, y+1/2, z+1/2)',
'(-x+1/2, y, z+1/2)', '(-x+1/2, y+1/2, z)',
'(-z, -x, -y)', '(-z, -x+1/2, -y+1/2)',
'(-z+1/2, -x, -y+1/2)', '(-z+1/2, -x+1/2, -y)',
'(-z, x, y)', '(-z, x+1/2, y+1/2)',
'(-z+1/2, x, y+1/2)', '(-z+1/2, x+1/2, y)',
'(z, x, -y)', '(z, x+1/2, -y+1/2)',
'(z+1/2, x, -y+1/2)', '(z+1/2, x+1/2, -y)',
'(z, -x, y)', '(z, -x+1/2, y+1/2)',
'(z+1/2, -x, y+1/2)', '(z+1/2, -x+1/2, y)',
'(-y, -z, -x)', '(-y, -z+1/2, -x+1/2)',
'(-y+1/2, -z, -x+1/2)', '(-y+1/2, -z+1/2, -x)',
'(y, -z, x)', '(y, -z+1/2, x+1/2)',
'(y+1/2, -z, x+1/2)', '(y+1/2, -z+1/2, x)',
'(-y, z, x)', '(-y, z+1/2, x+1/2)',
'(-y+1/2, z, x+1/2)', '(-y+1/2, z+1/2, x)',
'(y, z, -x)', '(y, z+1/2, -x+1/2)',
'(y+1/2, z, -x+1/2)', '(y+1/2, z+1/2, -x)',
'(-y, -x, z)', '(-y, -x+1/2, z+1/2)',
'(-y+1/2, -x, z+1/2)', '(-y+1/2, -x+1/2, z)',
'(y, x, z)', '(y, x+1/2, z+1/2)',
'(y+1/2, x, z+1/2)', '(y+1/2, x+1/2, z)',
'(-y, x, -z)', '(-y, x+1/2, -z+1/2)',
'(-y+1/2, x, -z+1/2)', '(-y+1/2, x+1/2, -z)',
'(y, -x, -z)', '(y, -x+1/2, -z+1/2)',
'(y+1/2, -x, -z+1/2)', '(y+1/2, -x+1/2, -z)',
'(-x, -z, y)', '(-x, -z+1/2, y+1/2)',
'(-x+1/2, -z, y+1/2)', '(-x+1/2, -z+1/2, y)',
'(x, -z, -y)', '(x, -z+1/2, -y+1/2)',
'(x+1/2, -z, -y+1/2)', '(x+1/2, -z+1/2, -y)',
'(x, z, y)', '(x, z+1/2, y+1/2)',
'(x+1/2, z, y+1/2)', '(x+1/2, z+1/2, y)',
'(-x, z, -y)', '(-x, z+1/2, -y+1/2)',
'(-x+1/2, z, -y+1/2)', '(-x+1/2, z+1/2, -y)',
'(-z, -y, x)', '(-z, -y+1/2, x+1/2)',
'(-z+1/2, -y, x+1/2)', '(-z+1/2, -y+1/2, x)',
'(-z, y, -x)', '(-z, y+1/2, -x+1/2)',
'(-z+1/2, y, -x+1/2)', '(-z+1/2, y+1/2, -x)',
'(z, -y, -x)', '(z, -y+1/2, -x+1/2)',
'(z+1/2, -y, -x+1/2)', '(z+1/2, -y+1/2, -x)',
'(z, y, x)', '(z, y+1/2, x+1/2)',
'(z+1/2, y, x+1/2)', '(z+1/2, y+1/2, x)'),
'hkl: h+k,h+l,k+l=2n, 0kl: k,l=2n, hhl: h+l=2n, '
'h00: h=2n')},
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'(0, 1/2, 1/4)', '(1/2, 0, 1/4)', '(1/2, 1/2, 3/4)'
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'(1/4, 1/4, 1/2)', '(1/4, 3/4, 0)'), 'hkl: h=2n'),
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'(1/2, 1/2, x+1/2)', '(1/2, 0, x)', '(0, 1/2, x)',
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'(1/4, x, 1/4)', '(1/4, x+1/2, 3/4)',
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'(3/4, 1/4, x+1/2)', '(3/4, 3/4, x)',
'(3/4, 1/4, -x)', '(3/4, 3/4, -x+1/2)',
'(1/4, 1/4, -x+1/2)', '(1/4, 3/4, -x)',
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'(-x+1/2, 3/4, 1/4)', '(-x+1/2, 1/4, 3/4)',
'(x, 1/4, 3/4)', '(x, 3/4, 1/4)',
'(x+1/2, 1/4, 1/4)', '(x+1/2, 3/4, 3/4)',
'(3/4, -x, 3/4)', '(3/4, -x+1/2, 1/4)',
'(1/4, -x, 1/4)', '(1/4, -x+1/2, 3/4)',
'(3/4, x, 1/4)', '(3/4, x+1/2, 3/4)',
'(1/4, x, 3/4)', '(1/4, x+1/2, 1/4)',
'(3/4, 3/4, -x)', '(3/4, 1/4, -x+1/2)',
'(1/4, 3/4, -x+1/2)', '(1/4, 1/4, -x)',
'(1/4, 3/4, x)', '(1/4, 1/4, x+1/2)',
'(3/4, 3/4, x+1/2)', '(3/4, 1/4, x)'), 'hkl: h=2n'),
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'(-x, -x, x)', '(-x, -x+1/2, x+1/2)',
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'(-x, x, -x)', '(-x, x+1/2, -x+1/2)',
'(-x+1/2, x, -x+1/2)', '(-x+1/2, x+1/2, -x)',
'(x, -x, -x)', '(x, -x+1/2, -x+1/2)',
'(x+1/2, -x, -x+1/2)', '(x+1/2, -x+1/2, -x)',
'(x+1/2, x+1/2, -x+1/2)', '(x+1/2, x, -x)',
'(x, x+1/2, -x)', '(x, x, -x+1/2)',
'(-x+1/2, -x+1/2, -x+1/2)', '(-x+1/2, -x, -x)',
'(-x, -x+1/2, -x)', '(-x, -x, -x+1/2)',
'(x+1/2, -x+1/2, x+1/2)', '(x+1/2, -x, x)',
'(x, -x+1/2, x)', '(x, -x, x+1/2)',
'(-x+1/2, x+1/2, x+1/2)', '(-x+1/2, x, x)',
'(-x, x+1/2, x)', '(-x, x, x+1/2)', '(-x, -x, -x)',
'(-x, -x+1/2, -x+1/2)', '(-x+1/2, -x, -x+1/2)',
'(-x+1/2, -x+1/2, -x)', '(x, x, -x)',
'(x, x+1/2, -x+1/2)', '(x+1/2, x, -x+1/2)',
'(x+1/2, x+1/2, -x)', '(x, -x, x)',
'(x, -x+1/2, x+1/2)', '(x+1/2, -x, x+1/2)',
'(x+1/2, -x+1/2, x)', '(-x, x, x)',
'(-x, x+1/2, x+1/2)', '(-x+1/2, x, x+1/2)',
'(-x+1/2, x+1/2, x)', '(-x+1/2, -x+1/2, x+1/2)',
'(-x+1/2, -x, x)', '(-x, -x+1/2, x)',
'(-x, -x, x+1/2)', '(x+1/2, x+1/2, x+1/2)',
'(x+1/2, x, x)', '(x, x+1/2, x)', '(x, x, x+1/2)',
'(-x+1/2, x+1/2, -x+1/2)', '(-x+1/2, x, -x)',
'(-x, x+1/2, -x)', '(-x, x, -x+1/2)',
'(x+1/2, -x+1/2, -x+1/2)', '(x+1/2, -x, -x)',
'(x, -x+1/2, -x)', '(x, -x, -x+1/2)'), 'hkl: h=2n'),
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'(3/4, y, y+1/2)', '(3/4, y+1/2, y)',
'(3/4, -y, y)', '(3/4, -y+1/2, y+1/2)',
'(1/4, -y, y+1/2)', '(1/4, -y+1/2, y)',
'(3/4, y, -y)', '(3/4, y+1/2, -y+1/2)',
'(1/4, y, -y+1/2)', '(1/4, y+1/2, -y)',
'(1/4, -y, -y)', '(1/4, -y+1/2, -y+1/2)',
'(3/4, -y, -y+1/2)', '(3/4, -y+1/2, -y)',
'(y, 1/4, y)', '(y, 3/4, y+1/2)',
'(y+1/2, 1/4, y+1/2)', '(y+1/2, 3/4, y)',
'(y, 3/4, -y)', '(y, 1/4, -y+1/2)',
'(y+1/2, 3/4, -y+1/2)', '(y+1/2, 1/4, -y)',
'(-y, 3/4, y)', '(-y, 1/4, y+1/2)',
'(-y+1/2, 3/4, y+1/2)', '(-y+1/2, 1/4, y)',
'(-y, 1/4, -y)', '(-y, 3/4, -y+1/2)',
'(-y+1/2, 1/4, -y+1/2)', '(-y+1/2, 3/4, -y)',
'(y, y, 1/4)', '(y, y+1/2, 3/4)', '(y+1/2, y, 3/4)',
'(y+1/2, y+1/2, 1/4)', '(-y, y, 3/4)',
'(-y, y+1/2, 1/4)', '(-y+1/2, y, 1/4)',
'(-y+1/2, y+1/2, 3/4)', '(y, -y, 3/4)',
'(y, -y+1/2, 1/4)', '(y+1/2, -y, 1/4)',
'(y+1/2, -y+1/2, 3/4)', '(-y, -y, 1/4)',
'(-y, -y+1/2, 3/4)', '(-y+1/2, -y, 3/4)',
'(-y+1/2, -y+1/2, 1/4)', '(3/4, -y, -y)',
'(3/4, -y+1/2, -y+1/2)', '(1/4, -y, -y+1/2)',
'(1/4, -y+1/2, -y)', '(1/4, y, -y)',
'(1/4, y+1/2, -y+1/2)', '(3/4, y, -y+1/2)',
'(3/4, y+1/2, -y)', '(1/4, -y, y)',
'(1/4, -y+1/2, y+1/2)', '(3/4, -y, y+1/2)',
'(3/4, -y+1/2, y)', '(3/4, y, y)',
'(3/4, y+1/2, y+1/2)', '(1/4, y, y+1/2)',
'(1/4, y+1/2, y)', '(-y, 3/4, -y)',
'(-y, 1/4, -y+1/2)', '(-y+1/2, 3/4, -y+1/2)',
'(-y+1/2, 1/4, -y)', '(-y, 1/4, y)',
'(-y, 3/4, y+1/2)', '(-y+1/2, 1/4, y+1/2)',
'(-y+1/2, 3/4, y)', '(y, 1/4, -y)',
'(y, 3/4, -y+1/2)', '(y+1/2, 1/4, -y+1/2)',
'(y+1/2, 3/4, -y)', '(y, 3/4, y)',
'(y, 1/4, y+1/2)', '(y+1/2, 3/4, y+1/2)',
'(y+1/2, 1/4, y)', '(-y, -y, 3/4)',
'(-y, -y+1/2, 1/4)', '(-y+1/2, -y, 1/4)',
'(-y+1/2, -y+1/2, 3/4)', '(y, -y, 1/4)',
'(y, -y+1/2, 3/4)', '(y+1/2, -y, 3/4)',
'(y+1/2, -y+1/2, 1/4)', '(-y, y, 1/4)',
'(-y, y+1/2, 3/4)', '(-y+1/2, y, 3/4)',
'(-y+1/2, y+1/2, 1/4)', '(y, y, 3/4)',
'(y, y+1/2, 1/4)', '(y+1/2, y, 1/4)',
'(y+1/2, y+1/2, 3/4)'), 'hkl: h=2n'),
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'(1/2, y+1/2, z)', '(0, -y, z)',
'(0, -y+1/2, z+1/2)', '(1/2, -y, z+1/2)',
'(1/2, -y+1/2, z)', '(0, y, -z)',
'(0, y+1/2, -z+1/2)', '(1/2, y, -z+1/2)',
'(1/2, y+1/2, -z)', '(0, -y, -z)',
'(0, -y+1/2, -z+1/2)', '(1/2, -y, -z+1/2)',
'(1/2, -y+1/2, -z)', '(z, 0, y)', '(z, 1/2, y+1/2)',
'(z+1/2, 0, y+1/2)', '(z+1/2, 1/2, y)',
'(z, 0, -y)', '(z, 1/2, -y+1/2)',
'(z+1/2, 0, -y+1/2)', '(z+1/2, 1/2, -y)',
'(-z, 0, y)', '(-z, 1/2, y+1/2)',
'(-z+1/2, 0, y+1/2)', '(-z+1/2, 1/2, y)',
'(-z, 0, -y)', '(-z, 1/2, -y+1/2)',
'(-z+1/2, 0, -y+1/2)', '(-z+1/2, 1/2, -y)',
'(y, z, 0)', '(y, z+1/2, 1/2)', '(y+1/2, z, 1/2)',
'(y+1/2, z+1/2, 0)', '(-y, z, 0)',
'(-y, z+1/2, 1/2)', '(-y+1/2, z, 1/2)',
'(-y+1/2, z+1/2, 0)', '(y, -z, 0)',
'(y, -z+1/2, 1/2)', '(y+1/2, -z, 1/2)',
'(y+1/2, -z+1/2, 0)', '(-y, -z, 0)',
'(-y, -z+1/2, 1/2)', '(-y+1/2, -z, 1/2)',
'(-y+1/2, -z+1/2, 0)', '(y+1/2, 1/2, -z+1/2)',
'(y+1/2, 0, -z)', '(y, 1/2, -z)', '(y, 0, -z+1/2)',
'(-y+1/2, 1/2, -z+1/2)', '(-y+1/2, 0, -z)',
'(-y, 1/2, -z)', '(-y, 0, -z+1/2)',
'(y+1/2, 1/2, z+1/2)', '(y+1/2, 0, z)',
'(y, 1/2, z)', '(y, 0, z+1/2)',
'(-y+1/2, 1/2, z+1/2)', '(-y+1/2, 0, z)',
'(-y, 1/2, z)', '(-y, 0, z+1/2)',
'(1/2, z+1/2, -y+1/2)', '(1/2, z, -y)',
'(0, z+1/2, -y)', '(0, z, -y+1/2)',
'(1/2, z+1/2, y+1/2)', '(1/2, z, y)',
'(0, z+1/2, y)', '(0, z, y+1/2)',
'(1/2, -z+1/2, -y+1/2)', '(1/2, -z, -y)',
'(0, -z+1/2, -y)', '(0, -z, -y+1/2)',
'(1/2, -z+1/2, y+1/2)', '(1/2, -z, y)',
'(0, -z+1/2, y)', '(0, -z, y+1/2)',
'(z+1/2, y+1/2, 1/2)', '(z+1/2, y, 0)',
'(z, y+1/2, 0)', '(z, y, 1/2)',
'(z+1/2, -y+1/2, 1/2)', '(z+1/2, -y, 0)',
'(z, -y+1/2, 0)', '(z, -y, 1/2)',
'(-z+1/2, y+1/2, 1/2)', '(-z+1/2, y, 0)',
'(-z, y+1/2, 0)', '(-z, y, 1/2)',
'(-z+1/2, -y+1/2, 1/2)', '(-z+1/2, -y, 0)',
'(-z, -y+1/2, 0)', '(-z, -y, 1/2)'), None),
'192j': (7, ('(x, y, z)', '(x, y+1/2, z+1/2)',
'(x+1/2, y, z+1/2)', '(x+1/2, y+1/2, z)',
'(-x, -y, z)', '(-x, -y+1/2, z+1/2)',
'(-x+1/2, -y, z+1/2)', '(-x+1/2, -y+1/2, z)',
'(-x, y, -z)', '(-x, y+1/2, -z+1/2)',
'(-x+1/2, y, -z+1/2)', '(-x+1/2, y+1/2, -z)',
'(x, -y, -z)', '(x, -y+1/2, -z+1/2)',
'(x+1/2, -y, -z+1/2)', '(x+1/2, -y+1/2, -z)',
'(z, x, y)', '(z, x+1/2, y+1/2)',
'(z+1/2, x, y+1/2)', '(z+1/2, x+1/2, y)',
'(z, -x, -y)', '(z, -x+1/2, -y+1/2)',
'(z+1/2, -x, -y+1/2)', '(z+1/2, -x+1/2, -y)',
'(-z, -x, y)', '(-z, -x+1/2, y+1/2)',
'(-z+1/2, -x, y+1/2)', '(-z+1/2, -x+1/2, y)',
'(-z, x, -y)', '(-z, x+1/2, -y+1/2)',
'(-z+1/2, x, -y+1/2)', '(-z+1/2, x+1/2, -y)',
'(y, z, x)', '(y, z+1/2, x+1/2)',
'(y+1/2, z, x+1/2)', '(y+1/2, z+1/2, x)',
'(-y, z, -x)', '(-y, z+1/2, -x+1/2)',
'(-y+1/2, z, -x+1/2)', '(-y+1/2, z+1/2, -x)',
'(y, -z, -x)', '(y, -z+1/2, -x+1/2)',
'(y+1/2, -z, -x+1/2)', '(y+1/2, -z+1/2, -x)',
'(-y, -z, x)', '(-y, -z+1/2, x+1/2)',
'(-y+1/2, -z, x+1/2)', '(-y+1/2, -z+1/2, x)',
'(y+1/2, x+1/2, -z+1/2)', '(y+1/2, x, -z)',
'(y, x+1/2, -z)', '(y, x, -z+1/2)',
'(-y+1/2, -x+1/2, -z+1/2)', '(-y+1/2, -x, -z)',
'(-y, -x+1/2, -z)', '(-y, -x, -z+1/2)',
'(y+1/2, -x+1/2, z+1/2)', '(y+1/2, -x, z)',
'(y, -x+1/2, z)', '(y, -x, z+1/2)',
'(-y+1/2, x+1/2, z+1/2)', '(-y+1/2, x, z)',
'(-y, x+1/2, z)', '(-y, x, z+1/2)',
'(x+1/2, z+1/2, -y+1/2)', '(x+1/2, z, -y)',
'(x, z+1/2, -y)', '(x, z, -y+1/2)',
'(-x+1/2, z+1/2, y+1/2)', '(-x+1/2, z, y)',
'(-x, z+1/2, y)', '(-x, z, y+1/2)',
'(-x+1/2, -z+1/2, -y+1/2)', '(-x+1/2, -z, -y)',
'(-x, -z+1/2, -y)', '(-x, -z, -y+1/2)',
'(x+1/2, -z+1/2, y+1/2)', '(x+1/2, -z, y)',
'(x, -z+1/2, y)', '(x, -z, y+1/2)',
'(z+1/2, y+1/2, -x+1/2)', '(z+1/2, y, -x)',
'(z, y+1/2, -x)', '(z, y, -x+1/2)',
'(z+1/2, -y+1/2, x+1/2)', '(z+1/2, -y, x)',
'(z, -y+1/2, x)', '(z, -y, x+1/2)',
'(-z+1/2, y+1/2, x+1/2)', '(-z+1/2, y, x)',
'(-z, y+1/2, x)', '(-z, y, x+1/2)',
'(-z+1/2, -y+1/2, -x+1/2)', '(-z+1/2, -y, -x)',
'(-z, -y+1/2, -x)', '(-z, -y, -x+1/2)',
'(-x, -y, -z)', '(-x, -y+1/2, -z+1/2)',
'(-x+1/2, -y, -z+1/2)', '(-x+1/2, -y+1/2, -z)',
'(x, y, -z)', '(x, y+1/2, -z+1/2)',
'(x+1/2, y, -z+1/2)', '(x+1/2, y+1/2, -z)',
'(x, -y, z)', '(x, -y+1/2, z+1/2)',
'(x+1/2, -y, z+1/2)', '(x+1/2, -y+1/2, z)',
'(-x, y, z)', '(-x, y+1/2, z+1/2)',
'(-x+1/2, y, z+1/2)', '(-x+1/2, y+1/2, z)',
'(-z, -x, -y)', '(-z, -x+1/2, -y+1/2)',
'(-z+1/2, -x, -y+1/2)', '(-z+1/2, -x+1/2, -y)',
'(-z, x, y)', '(-z, x+1/2, y+1/2)',
'(-z+1/2, x, y+1/2)', '(-z+1/2, x+1/2, y)',
'(z, x, -y)', '(z, x+1/2, -y+1/2)',
'(z+1/2, x, -y+1/2)', '(z+1/2, x+1/2, -y)',
'(z, -x, y)', '(z, -x+1/2, y+1/2)',
'(z+1/2, -x, y+1/2)', '(z+1/2, -x+1/2, y)',
'(-y, -z, -x)', '(-y, -z+1/2, -x+1/2)',
'(-y+1/2, -z, -x+1/2)', '(-y+1/2, -z+1/2, -x)',
'(y, -z, x)', '(y, -z+1/2, x+1/2)',
'(y+1/2, -z, x+1/2)', '(y+1/2, -z+1/2, x)',
'(-y, z, x)', '(-y, z+1/2, x+1/2)',
'(-y+1/2, z, x+1/2)', '(-y+1/2, z+1/2, x)',
'(y, z, -x)', '(y, z+1/2, -x+1/2)',
'(y+1/2, z, -x+1/2)', '(y+1/2, z+1/2, -x)',
'(-y+1/2, -x+1/2, z+1/2)', '(-y+1/2, -x, z)',
'(-y, -x+1/2, z)', '(-y, -x, z+1/2)',
'(y+1/2, x+1/2, z+1/2)', '(y+1/2, x, z)',
'(y, x+1/2, z)', '(y, x, z+1/2)',
'(-y+1/2, x+1/2, -z+1/2)', '(-y+1/2, x, -z)',
'(-y, x+1/2, -z)', '(-y, x, -z+1/2)',
'(y+1/2, -x+1/2, -z+1/2)', '(y+1/2, -x, -z)',
'(y, -x+1/2, -z)', '(y, -x, -z+1/2)',
'(-x+1/2, -z+1/2, y+1/2)', '(-x+1/2, -z, y)',
'(-x, -z+1/2, y)', '(-x, -z, y+1/2)',
'(x+1/2, -z+1/2, -y+1/2)', '(x+1/2, -z, -y)',
'(x, -z+1/2, -y)', '(x, -z, -y+1/2)',
'(x+1/2, z+1/2, y+1/2)', '(x+1/2, z, y)',
'(x, z+1/2, y)', '(x, z, y+1/2)',
'(-x+1/2, z+1/2, -y+1/2)', '(-x+1/2, z, -y)',
'(-x, z+1/2, -y)', '(-x, z, -y+1/2)',
'(-z+1/2, -y+1/2, x+1/2)', '(-z+1/2, -y, x)',
'(-z, -y+1/2, x)', '(-z, -y, x+1/2)',
'(-z+1/2, y+1/2, -x+1/2)', '(-z+1/2, y, -x)',
'(-z, y+1/2, -x)', '(-z, y, -x+1/2)',
'(z+1/2, -y+1/2, -x+1/2)', '(z+1/2, -y, -x)',
'(z, -y+1/2, -x)', '(z, -y, -x+1/2)',
'(z+1/2, y+1/2, x+1/2)', '(z+1/2, y, x)',
'(z, y+1/2, x)', '(z, y, x+1/2)'),
'hkl: h+k=2n, h+l,k+l=2n, 0kl: k,l=2n, hhl: h,l=2n, '
'h00: h=2n')},
'227:1': {'8a': (0, ('(0, 0, 0)', '(0, 1/2, 1/2)', '(1/2, 0, 1/2)',
'(1/2, 1/2, 0)', '(3/4, 1/4, 3/4)',
'(3/4, 3/4, 1/4)', '(1/4, 1/4, 1/4)',
'(1/4, 3/4, 3/4)'), 'hkl: h=2n+1 or h+k+l=4n'),
'8b': (0, ('(1/2, 1/2, 1/2)', '(1/2, 0, 0)', '(0, 1/2, 0)',
'(0, 0, 1/2)', '(1/4, 3/4, 1/4)',
'(1/4, 1/4, 3/4)', '(3/4, 3/4, 3/4)',
'(3/4, 1/4, 1/4)'), 'hkl: h=2n+1 or h+k+l=4n'),
'16c': (0, ('(1/8, 1/8, 1/8)', '(1/8, 5/8, 5/8)',
'(5/8, 1/8, 5/8)', '(5/8, 5/8, 1/8)',
'(7/8, 3/8, 5/8)', '(7/8, 7/8, 1/8)',
'(3/8, 3/8, 1/8)', '(3/8, 7/8, 5/8)',
'(3/8, 5/8, 7/8)', '(3/8, 1/8, 3/8)',
'(7/8, 5/8, 3/8)', '(7/8, 1/8, 7/8)',
'(5/8, 7/8, 3/8)', '(5/8, 3/8, 7/8)',
'(1/8, 7/8, 7/8)', '(1/8, 3/8, 3/8)'),
'hkl: h=2n+1 or h,k,l=4n+2 or h,k,l=4n'),
'16d': (0, ('(5/8, 5/8, 5/8)', '(5/8, 1/8, 1/8)',
'(1/8, 5/8, 1/8)', '(1/8, 1/8, 5/8)',
'(3/8, 7/8, 1/8)', '(3/8, 3/8, 5/8)',
'(7/8, 7/8, 5/8)', '(7/8, 3/8, 1/8)',
'(7/8, 1/8, 3/8)', '(7/8, 5/8, 7/8)',
'(3/8, 1/8, 7/8)', '(3/8, 5/8, 3/8)',
'(1/8, 3/8, 7/8)', '(1/8, 7/8, 3/8)',
'(5/8, 3/8, 3/8)', '(5/8, 7/8, 7/8)'),
'hkl: h=2n+1 or h,k,l=4n+2 or h,k,l=4n'),
'32e': (1, ('(x, x, x)', '(x, x+1/2, x+1/2)',
'(x+1/2, x, x+1/2)', '(x+1/2, x+1/2, x)',
'(-x, -x+1/2, x+1/2)', '(-x, -x, x)',
'(-x+1/2, -x+1/2, x)', '(-x+1/2, -x, x+1/2)',
'(-x+1/2, x+1/2, -x)', '(-x+1/2, x, -x+1/2)',
'(-x, x+1/2, -x+1/2)', '(-x, x, -x)',
'(x+1/2, -x, -x+1/2)', '(x+1/2, -x+1/2, -x)',
'(x, -x, -x)', '(x, -x+1/2, -x+1/2)',
'(x+3/4, x+1/4, -x+3/4)',
'(x+3/4, x+3/4, -x+1/4)',
'(x+1/4, x+1/4, -x+1/4)',
'(x+1/4, x+3/4, -x+3/4)',
'(-x+1/4, -x+1/4, -x+1/4)',
'(-x+1/4, -x+3/4, -x+3/4)',
'(-x+3/4, -x+1/4, -x+3/4)',
'(-x+3/4, -x+3/4, -x+1/4)',
'(x+1/4, -x+3/4, x+3/4)',
'(x+1/4, -x+1/4, x+1/4)',
'(x+3/4, -x+3/4, x+1/4)',
'(x+3/4, -x+1/4, x+3/4)',
'(-x+3/4, x+3/4, x+1/4)',
'(-x+3/4, x+1/4, x+3/4)',
'(-x+1/4, x+3/4, x+3/4)',
'(-x+1/4, x+1/4, x+1/4)'),
'no extra conditions, no extra conditions'),
'48f': (1, ('(x, 0, 0)', '(x, 1/2, 1/2)', '(x+1/2, 0, 1/2)',
'(x+1/2, 1/2, 0)', '(-x, 1/2, 1/2)', '(-x, 0, 0)',
'(-x+1/2, 1/2, 0)', '(-x+1/2, 0, 1/2)',
'(0, x, 0)', '(0, x+1/2, 1/2)', '(1/2, x, 1/2)',
'(1/2, x+1/2, 0)', '(1/2, -x, 1/2)',
'(1/2, -x+1/2, 0)', '(0, -x, 0)',
'(0, -x+1/2, 1/2)', '(0, 0, x)',
'(0, 1/2, x+1/2)', '(1/2, 0, x+1/2)',
'(1/2, 1/2, x)', '(1/2, 1/2, -x)',
'(1/2, 0, -x+1/2)', '(0, 1/2, -x+1/2)',
'(0, 0, -x)', '(3/4, x+1/4, 3/4)',
'(3/4, x+3/4, 1/4)', '(1/4, x+1/4, 1/4)',
'(1/4, x+3/4, 3/4)', '(1/4, -x+1/4, 1/4)',
'(1/4, -x+3/4, 3/4)', '(3/4, -x+1/4, 3/4)',
'(3/4, -x+3/4, 1/4)', '(x+3/4, 1/4, 3/4)',
'(x+3/4, 3/4, 1/4)', '(x+1/4, 1/4, 1/4)',
'(x+1/4, 3/4, 3/4)', '(-x+3/4, 3/4, 1/4)',
'(-x+3/4, 1/4, 3/4)', '(-x+1/4, 3/4, 3/4)',
'(-x+1/4, 1/4, 1/4)', '(3/4, 1/4, -x+3/4)',
'(3/4, 3/4, -x+1/4)', '(1/4, 1/4, -x+1/4)',
'(1/4, 3/4, -x+3/4)', '(1/4, 3/4, x+3/4)',
'(1/4, 1/4, x+1/4)', '(3/4, 3/4, x+1/4)',
'(3/4, 1/4, x+3/4)'), 'hkl: h=2n+1 or h+k+l=4n'),
'96g': (5, ('(x, x, z)', '(x, x+1/2, z+1/2)',
'(x+1/2, x, z+1/2)', '(x+1/2, x+1/2, z)',
'(-x, -x+1/2, z+1/2)', '(-x, -x, z)',
'(-x+1/2, -x+1/2, z)', '(-x+1/2, -x, z+1/2)',
'(-x+1/2, x+1/2, -z)', '(-x+1/2, x, -z+1/2)',
'(-x, x+1/2, -z+1/2)', '(-x, x, -z)',
'(x+1/2, -x, -z+1/2)', '(x+1/2, -x+1/2, -z)',
'(x, -x, -z)', '(x, -x+1/2, -z+1/2)', '(z, x, x)',
'(z, x+1/2, x+1/2)', '(z+1/2, x, x+1/2)',
'(z+1/2, x+1/2, x)', '(z+1/2, -x, -x+1/2)',
'(z+1/2, -x+1/2, -x)', '(z, -x, -x)',
'(z, -x+1/2, -x+1/2)', '(-z, -x+1/2, x+1/2)',
'(-z, -x, x)', '(-z+1/2, -x+1/2, x)',
'(-z+1/2, -x, x+1/2)', '(-z+1/2, x+1/2, -x)',
'(-z+1/2, x, -x+1/2)', '(-z, x+1/2, -x+1/2)',
'(-z, x, -x)', '(x, z, x)', '(x, z+1/2, x+1/2)',
'(x+1/2, z, x+1/2)', '(x+1/2, z+1/2, x)',
'(-x+1/2, z+1/2, -x)', '(-x+1/2, z, -x+1/2)',
'(-x, z+1/2, -x+1/2)', '(-x, z, -x)',
'(x+1/2, -z, -x+1/2)', '(x+1/2, -z+1/2, -x)',
'(x, -z, -x)', '(x, -z+1/2, -x+1/2)',
'(-x, -z+1/2, x+1/2)', '(-x, -z, x)',
'(-x+1/2, -z+1/2, x)', '(-x+1/2, -z, x+1/2)',
'(x+3/4, x+1/4, -z+3/4)',
'(x+3/4, x+3/4, -z+1/4)',
'(x+1/4, x+1/4, -z+1/4)',
'(x+1/4, x+3/4, -z+3/4)',
'(-x+1/4, -x+1/4, -z+1/4)',
'(-x+1/4, -x+3/4, -z+3/4)',
'(-x+3/4, -x+1/4, -z+3/4)',
'(-x+3/4, -x+3/4, -z+1/4)',
'(x+1/4, -x+3/4, z+3/4)',
'(x+1/4, -x+1/4, z+1/4)',
'(x+3/4, -x+3/4, z+1/4)',
'(x+3/4, -x+1/4, z+3/4)',
'(-x+3/4, x+3/4, z+1/4)',
'(-x+3/4, x+1/4, z+3/4)',
'(-x+1/4, x+3/4, z+3/4)',
'(-x+1/4, x+1/4, z+1/4)',
'(x+3/4, z+1/4, -x+3/4)',
'(x+3/4, z+3/4, -x+1/4)',
'(x+1/4, z+1/4, -x+1/4)',
'(x+1/4, z+3/4, -x+3/4)',
'(-x+3/4, z+3/4, x+1/4)',
'(-x+3/4, z+1/4, x+3/4)',
'(-x+1/4, z+3/4, x+3/4)',
'(-x+1/4, z+1/4, x+1/4)',
'(-x+1/4, -z+1/4, -x+1/4)',
'(-x+1/4, -z+3/4, -x+3/4)',
'(-x+3/4, -z+1/4, -x+3/4)',
'(-x+3/4, -z+3/4, -x+1/4)',
'(x+1/4, -z+3/4, x+3/4)',
'(x+1/4, -z+1/4, x+1/4)',
'(x+3/4, -z+3/4, x+1/4)',
'(x+3/4, -z+1/4, x+3/4)',
'(z+3/4, x+1/4, -x+3/4)',
'(z+3/4, x+3/4, -x+1/4)',
'(z+1/4, x+1/4, -x+1/4)',
'(z+1/4, x+3/4, -x+3/4)',
'(z+1/4, -x+3/4, x+3/4)',
'(z+1/4, -x+1/4, x+1/4)',
'(z+3/4, -x+3/4, x+1/4)',
'(z+3/4, -x+1/4, x+3/4)',
'(-z+3/4, x+3/4, x+1/4)',
'(-z+3/4, x+1/4, x+3/4)',
'(-z+1/4, x+3/4, x+3/4)',
'(-z+1/4, x+1/4, x+1/4)',
'(-z+1/4, -x+1/4, -x+1/4)',
'(-z+1/4, -x+3/4, -x+3/4)',
'(-z+3/4, -x+1/4, -x+3/4)',
'(-z+3/4, -x+3/4, -x+1/4)'), None),
'96h': (2, ('(1/8, y, -y+1/4)', '(1/8, y+1/2, -y+3/4)',
'(5/8, y, -y+3/4)', '(5/8, y+1/2, -y+1/4)',
'(7/8, -y+1/2, -y+3/4)', '(7/8, -y, -y+1/4)',
'(3/8, -y+1/2, -y+1/4)', '(3/8, -y, -y+3/4)',
'(3/8, y+1/2, y+3/4)', '(3/8, y, y+1/4)',
'(7/8, y+1/2, y+1/4)', '(7/8, y, y+3/4)',
'(5/8, -y, y+1/4)', '(5/8, -y+1/2, y+3/4)',
'(1/8, -y, y+3/4)', '(1/8, -y+1/2, y+1/4)',
'(-y+1/4, 1/8, y)', '(-y+1/4, 5/8, y+1/2)',
'(-y+3/4, 1/8, y+1/2)', '(-y+3/4, 5/8, y)',
'(-y+3/4, 7/8, -y+1/2)', '(-y+3/4, 3/8, -y)',
'(-y+1/4, 7/8, -y)', '(-y+1/4, 3/8, -y+1/2)',
'(y+3/4, 3/8, y+1/2)', '(y+3/4, 7/8, y)',
'(y+1/4, 3/8, y)', '(y+1/4, 7/8, y+1/2)',
'(y+1/4, 5/8, -y)', '(y+1/4, 1/8, -y+1/2)',
'(y+3/4, 5/8, -y+1/2)', '(y+3/4, 1/8, -y)',
'(y, -y+1/4, 1/8)', '(y, -y+3/4, 5/8)',
'(y+1/2, -y+1/4, 5/8)', '(y+1/2, -y+3/4, 1/8)',
'(-y+1/2, -y+3/4, 7/8)', '(-y+1/2, -y+1/4, 3/8)',
'(-y, -y+3/4, 3/8)', '(-y, -y+1/4, 7/8)',
'(y+1/2, y+3/4, 3/8)', '(y+1/2, y+1/4, 7/8)',
'(y, y+3/4, 7/8)', '(y, y+1/4, 3/8)',
'(-y, y+1/4, 5/8)', '(-y, y+3/4, 1/8)',
'(-y+1/2, y+1/4, 1/8)', '(-y+1/2, y+3/4, 5/8)',
'(1/8, -y+1/4, y)', '(1/8, -y+3/4, y+1/2)',
'(5/8, -y+1/4, y+1/2)', '(5/8, -y+3/4, y)',
'(3/8, y+3/4, y+1/2)', '(3/8, y+1/4, y)',
'(7/8, y+3/4, y)', '(7/8, y+1/4, y+1/2)',
'(7/8, -y+3/4, -y+1/2)', '(7/8, -y+1/4, -y)',
'(3/8, -y+3/4, -y)', '(3/8, -y+1/4, -y+1/2)',
'(5/8, y+1/4, -y)', '(5/8, y+3/4, -y+1/2)',
'(1/8, y+1/4, -y+1/2)', '(1/8, y+3/4, -y)',
'(y, 1/8, -y+1/4)', '(y, 5/8, -y+3/4)',
'(y+1/2, 1/8, -y+3/4)', '(y+1/2, 5/8, -y+1/4)',
'(y+1/2, 3/8, y+3/4)', '(y+1/2, 7/8, y+1/4)',
'(y, 3/8, y+1/4)', '(y, 7/8, y+3/4)',
'(-y+1/2, 7/8, -y+3/4)', '(-y+1/2, 3/8, -y+1/4)',
'(-y, 7/8, -y+1/4)', '(-y, 3/8, -y+3/4)',
'(-y, 5/8, y+1/4)', '(-y, 1/8, y+3/4)',
'(-y+1/2, 5/8, y+3/4)', '(-y+1/2, 1/8, y+1/4)',
'(-y+1/4, y, 1/8)', '(-y+1/4, y+1/2, 5/8)',
'(-y+3/4, y, 5/8)', '(-y+3/4, y+1/2, 1/8)',
'(y+3/4, y+1/2, 3/8)', '(y+3/4, y, 7/8)',
'(y+1/4, y+1/2, 7/8)', '(y+1/4, y, 3/8)',
'(-y+3/4, -y+1/2, 7/8)', '(-y+3/4, -y, 3/8)',
'(-y+1/4, -y+1/2, 3/8)', '(-y+1/4, -y, 7/8)',
'(y+1/4, -y, 5/8)', '(y+1/4, -y+1/2, 1/8)',
'(y+3/4, -y, 1/8)', '(y+3/4, -y+1/2, 5/8)'), None
),
'192i': (7, ('(x, y, z)', '(x, y+1/2, z+1/2)',
'(x+1/2, y, z+1/2)', '(x+1/2, y+1/2, z)',
'(-x, -y+1/2, z+1/2)', '(-x, -y, z)',
'(-x+1/2, -y+1/2, z)', '(-x+1/2, -y, z+1/2)',
'(-x+1/2, y+1/2, -z)', '(-x+1/2, y, -z+1/2)',
'(-x, y+1/2, -z+1/2)', '(-x, y, -z)',
'(x+1/2, -y, -z+1/2)', '(x+1/2, -y+1/2, -z)',
'(x, -y, -z)', '(x, -y+1/2, -z+1/2)',
'(z, x, y)', '(z, x+1/2, y+1/2)',
'(z+1/2, x, y+1/2)', '(z+1/2, x+1/2, y)',
'(z+1/2, -x, -y+1/2)', '(z+1/2, -x+1/2, -y)',
'(z, -x, -y)', '(z, -x+1/2, -y+1/2)',
'(-z, -x+1/2, y+1/2)', '(-z, -x, y)',
'(-z+1/2, -x+1/2, y)', '(-z+1/2, -x, y+1/2)',
'(-z+1/2, x+1/2, -y)', '(-z+1/2, x, -y+1/2)',
'(-z, x+1/2, -y+1/2)', '(-z, x, -y)',
'(y, z, x)', '(y, z+1/2, x+1/2)',
'(y+1/2, z, x+1/2)', '(y+1/2, z+1/2, x)',
'(-y+1/2, z+1/2, -x)', '(-y+1/2, z, -x+1/2)',
'(-y, z+1/2, -x+1/2)', '(-y, z, -x)',
'(y+1/2, -z, -x+1/2)', '(y+1/2, -z+1/2, -x)',
'(y, -z, -x)', '(y, -z+1/2, -x+1/2)',
'(-y, -z+1/2, x+1/2)', '(-y, -z, x)',
'(-y+1/2, -z+1/2, x)', '(-y+1/2, -z, x+1/2)',
'(y+3/4, x+1/4, -z+3/4)',
'(y+3/4, x+3/4, -z+1/4)',
'(y+1/4, x+1/4, -z+1/4)',
'(y+1/4, x+3/4, -z+3/4)',
'(-y+1/4, -x+1/4, -z+1/4)',
'(-y+1/4, -x+3/4, -z+3/4)',
'(-y+3/4, -x+1/4, -z+3/4)',
'(-y+3/4, -x+3/4, -z+1/4)',
'(y+1/4, -x+3/4, z+3/4)',
'(y+1/4, -x+1/4, z+1/4)',
'(y+3/4, -x+3/4, z+1/4)',
'(y+3/4, -x+1/4, z+3/4)',
'(-y+3/4, x+3/4, z+1/4)',
'(-y+3/4, x+1/4, z+3/4)',
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'(y+1/4, -y+3/4, 1/2)', '(y+1/4, -y+1/4, 0)',
'(y+3/4, -y+3/4, 0)', '(y+3/4, -y+1/4, 1/2)'),
'n/a'),
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'(x+1/2, y, z+1/2)', '(x+1/2, y+1/2, z)',
'(-x+3/4, -y+1/4, z+1/2)', '(-x+3/4, -y+3/4, z)',
'(-x+1/4, -y+1/4, z)', '(-x+1/4, -y+3/4, z+1/2)',
'(-x+1/4, y+1/2, -z+3/4)', '(-x+1/4, y, -z+1/4)',
'(-x+3/4, y+1/2, -z+1/4)', '(-x+3/4, y, -z+3/4)',
'(x+1/2, -y+3/4, -z+1/4)',
'(x+1/2, -y+1/4, -z+3/4)', '(x, -y+3/4, -z+3/4)',
'(x, -y+1/4, -z+1/4)', '(z, x, y)',
'(z, x+1/2, y+1/2)', '(z+1/2, x, y+1/2)',
'(z+1/2, x+1/2, y)', '(z+1/2, -x+3/4, -y+1/4)',
'(z+1/2, -x+1/4, -y+3/4)', '(z, -x+3/4, -y+3/4)',
'(z, -x+1/4, -y+1/4)', '(-z+3/4, -x+1/4, y+1/2)',
'(-z+3/4, -x+3/4, y)', '(-z+1/4, -x+1/4, y)',
'(-z+1/4, -x+3/4, y+1/2)',
'(-z+1/4, x+1/2, -y+3/4)', '(-z+1/4, x, -y+1/4)',
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'(y+1/2, z, x+1/2)', '(y+1/2, z+1/2, x)',
'(-y+1/4, z+1/2, -x+3/4)', '(-y+1/4, z, -x+1/4)',
'(-y+3/4, z+1/2, -x+1/4)', '(-y+3/4, z, -x+3/4)',
'(y+1/2, -z+3/4, -x+1/4)',
'(y+1/2, -z+1/4, -x+3/4)', '(y, -z+3/4, -x+3/4)',
'(y, -z+1/4, -x+1/4)', '(-y+3/4, -z+1/4, x+1/2)',
'(-y+3/4, -z+3/4, x)', '(-y+1/4, -z+1/4, x)',
'(-y+1/4, -z+3/4, x+1/2)',
'(y+3/4, x+1/4, -z+1/2)', '(y+3/4, x+3/4, -z)',
'(y+1/4, x+1/4, -z)', '(y+1/4, x+3/4, -z+1/2)',
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'(-y+1/2, -x, -z+1/2)', '(-y+1/2, -x+1/2, -z)',
'(y+1/4, -x+1/2, z+3/4)', '(y+1/4, -x, z+1/4)',
'(y+3/4, -x+1/2, z+1/4)', '(y+3/4, -x, z+3/4)',
'(-y+1/2, x+3/4, z+1/4)',
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'(-y, x+1/4, z+1/4)', '(x+3/4, z+1/4, -y+1/2)',
'(x+3/4, z+3/4, -y)', '(x+1/4, z+1/4, -y)',
'(x+1/4, z+3/4, -y+1/2)',
'(-x+1/2, z+3/4, y+1/4)',
'(-x+1/2, z+1/4, y+3/4)', '(-x, z+3/4, y+3/4)',
'(-x, z+1/4, y+1/4)', '(-x, -z, -y)',
'(-x, -z+1/2, -y+1/2)', '(-x+1/2, -z, -y+1/2)',
'(-x+1/2, -z+1/2, -y)', '(x+1/4, -z+1/2, y+3/4)',
'(x+1/4, -z, y+1/4)', '(x+3/4, -z+1/2, y+1/4)',
'(x+3/4, -z, y+3/4)', '(z+3/4, y+1/4, -x+1/2)',
'(z+3/4, y+3/4, -x)', '(z+1/4, y+1/4, -x)',
'(z+1/4, y+3/4, -x+1/2)',
'(z+1/4, -y+1/2, x+3/4)', '(z+1/4, -y, x+1/4)',
'(z+3/4, -y+1/2, x+1/4)', '(z+3/4, -y, x+3/4)',
'(-z+1/2, y+3/4, x+1/4)',
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'(-z+1/2, -y+1/2, -x)', '(-x, -y, -z)',
'(-x, -y+1/2, -z+1/2)', '(-x+1/2, -y, -z+1/2)',
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'(x+1/4, y+1/4, -z)', '(x+3/4, y+3/4, -z)',
'(x+3/4, y+1/4, -z+1/2)',
'(x+3/4, -y+1/2, z+1/4)', '(x+3/4, -y, z+3/4)',
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'(-x+1/2, y+1/4, z+3/4)',
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'(z+3/4, x+1/4, -y+1/2)',
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'(-x+3/4, -z+1/4, y+1/2)',
'(x+1/2, -z+1/4, -y+3/4)',
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'(z, -y+3/4, -x+3/4)', '(z, y, x)',
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'(1/2, 1/2, 1/2)', '(1/2, 0, 0)'), 'hkl: h+k+l=4n'
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'(1/8, 7/8, 3/8)', '(1/8, 3/8, 7/8)',
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'(7/8, 3/8, 7/8)', '(7/8, 7/8, 3/8)',
'(5/8, 1/8, 7/8)', '(5/8, 5/8, 3/8)',
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'(1/8, 7/8, 5/8)', '(1/8, 3/8, 1/8)',
'(5/8, 7/8, 1/8)', '(5/8, 3/8, 5/8)',
'(7/8, 5/8, 1/8)', '(7/8, 1/8, 5/8)',
'(3/8, 5/8, 5/8)', '(3/8, 1/8, 1/8)',
'(1/8, 5/8, 3/8)', '(1/8, 1/8, 7/8)',
'(5/8, 5/8, 7/8)', '(5/8, 1/8, 3/8)',
'(7/8, 7/8, 7/8)', '(7/8, 3/8, 3/8)',
'(3/8, 7/8, 3/8)', '(3/8, 3/8, 7/8)',
'(5/8, 3/8, 1/8)', '(5/8, 7/8, 5/8)',
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'(3/8, 1/8, 5/8)', '(3/8, 5/8, 1/8)',
'(7/8, 1/8, 1/8)', '(7/8, 5/8, 5/8)'),
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'(x+3/4, x+1/4, -x+3/4)',
'(x+3/4, x+3/4, -x+1/4)',
'(x+1/4, x+1/4, -x+1/4)',
'(x+1/4, x+3/4, -x+3/4)',
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'(x+1/4, -x+3/4, x+3/4)',
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'(x+3/4, -x+3/4, x+1/4)',
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'(-x+3/4, x+3/4, x+1/4)',
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'(x, 0, 1/2)', '(x, 1/2, 0)', '(x+1/2, 0, 0)',
'(x+1/2, 1/2, 1/2)', '(0, 1/2, x)',
'(0, 0, x+1/2)', '(1/2, 1/2, x+1/2)',
'(1/2, 0, x)', '(1/2, 0, -x)',
'(1/2, 1/2, -x+1/2)', '(0, 0, -x+1/2)',
'(0, 1/2, -x)'), 'hkl: h+k+l=4n'),
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'(5/8, y, -y+3/4)', '(5/8, y+1/2, -y+1/4)',
'(7/8, -y+1/2, -y+3/4)', '(7/8, -y, -y+1/4)',
'(3/8, -y+1/2, -y+1/4)', '(3/8, -y, -y+3/4)',
'(3/8, y+1/2, y+3/4)', '(3/8, y, y+1/4)',
'(7/8, y+1/2, y+1/4)', '(7/8, y, y+3/4)',
'(5/8, -y, y+1/4)', '(5/8, -y+1/2, y+3/4)',
'(1/8, -y, y+3/4)', '(1/8, -y+1/2, y+1/4)',
'(-y+1/4, 1/8, y)', '(-y+1/4, 5/8, y+1/2)',
'(-y+3/4, 1/8, y+1/2)', '(-y+3/4, 5/8, y)',
'(-y+3/4, 7/8, -y+1/2)', '(-y+3/4, 3/8, -y)',
'(-y+1/4, 7/8, -y)', '(-y+1/4, 3/8, -y+1/2)',
'(y+3/4, 3/8, y+1/2)', '(y+3/4, 7/8, y)',
'(y+1/4, 3/8, y)', '(y+1/4, 7/8, y+1/2)',
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'(-y+1/2, -y+3/4, 7/8)', '(-y+1/2, -y+1/4, 3/8)',
'(-y, -y+3/4, 3/8)', '(-y, -y+1/4, 7/8)',
'(y+1/2, y+3/4, 3/8)', '(y+1/2, y+1/4, 7/8)',
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'(-y+1/2, y+1/4, 1/8)', '(-y+1/2, y+3/4, 5/8)',
'(5/8, -y+3/4, y+1/2)', '(5/8, -y+1/4, y)',
'(1/8, -y+3/4, y)', '(1/8, -y+1/4, y+1/2)',
'(7/8, y+1/4, y)', '(7/8, y+3/4, y+1/2)',
'(3/8, y+1/4, y+1/2)', '(3/8, y+3/4, y)',
'(3/8, -y+1/4, -y)', '(3/8, -y+3/4, -y+1/2)',
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'(y, 5/8, -y+1/4)', '(y, 1/8, -y+3/4)',
'(y, 7/8, y+1/4)', '(y, 3/8, y+3/4)',
'(y+1/2, 7/8, y+3/4)', '(y+1/2, 3/8, y+1/4)',
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'(-y, 1/8, y+1/4)', '(-y, 5/8, y+3/4)',
'(-y+3/4, y+1/2, 5/8)', '(-y+3/4, y, 1/8)',
'(-y+1/4, y+1/2, 1/8)', '(-y+1/4, y, 5/8)',
'(y+1/4, y, 7/8)', '(y+1/4, y+1/2, 3/8)',
'(y+3/4, y, 3/8)', '(y+3/4, y+1/2, 7/8)',
'(-y+1/4, -y, 3/8)', '(-y+1/4, -y+1/2, 7/8)',
'(-y+3/4, -y, 7/8)', '(-y+3/4, -y+1/2, 3/8)',
'(y+3/4, -y+1/2, 1/8)', '(y+3/4, -y, 5/8)',
'(y+1/4, -y+1/2, 5/8)', '(y+1/4, -y, 1/8)'), None
),
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'(-x, y+1/2, -z+1/2)', '(-x, y, -z)',
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'(x, -y, -z)', '(x, -y+1/2, -z+1/2)',
'(z, x, y)', '(z, x+1/2, y+1/2)',
'(z+1/2, x, y+1/2)', '(z+1/2, x+1/2, y)',
'(z+1/2, -x, -y+1/2)', '(z+1/2, -x+1/2, -y)',
'(z, -x, -y)', '(z, -x+1/2, -y+1/2)',
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'(y, z, x)', '(y, z+1/2, x+1/2)',
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'(y+3/4, x+1/4, -z+3/4)',
'(y+3/4, x+3/4, -z+1/4)',
'(y+1/4, x+1/4, -z+1/4)',
'(y+1/4, x+3/4, -z+3/4)',
'(-y+1/4, -x+1/4, -z+1/4)',
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'(-y+3/4, -x+3/4, -z+1/4)',
'(y+1/4, -x+3/4, z+3/4)',
'(y+1/4, -x+1/4, z+1/4)',
'(y+3/4, -x+3/4, z+1/4)',
'(y+3/4, -x+1/4, z+3/4)',
'(-y+3/4, x+3/4, z+1/4)',
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'(-y+1/4, x+3/4, z+3/4)',
'(-y+1/4, x+1/4, z+1/4)',
'(x+3/4, z+1/4, -y+3/4)',
'(x+3/4, z+3/4, -y+1/4)',
'(x+1/4, z+1/4, -y+1/4)',
'(x+1/4, z+3/4, -y+3/4)',
'(-x+3/4, z+3/4, y+1/4)',
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'(-x+1/4, z+3/4, y+3/4)',
'(-x+1/4, z+1/4, y+1/4)',
'(-x+1/4, -z+1/4, -y+1/4)',
'(-x+1/4, -z+3/4, -y+3/4)',
'(-x+3/4, -z+1/4, -y+3/4)',
'(-x+3/4, -z+3/4, -y+1/4)',
'(x+1/4, -z+3/4, y+3/4)',
'(x+1/4, -z+1/4, y+1/4)',
'(x+3/4, -z+3/4, y+1/4)',
'(x+3/4, -z+1/4, y+3/4)',
'(z+3/4, y+1/4, -x+3/4)',
'(z+3/4, y+3/4, -x+1/4)',
'(z+1/4, y+1/4, -x+1/4)',
'(z+1/4, y+3/4, -x+3/4)',
'(z+1/4, -y+3/4, x+3/4)',
'(z+1/4, -y+1/4, x+1/4)',
'(z+3/4, -y+3/4, x+1/4)',
'(z+3/4, -y+1/4, x+3/4)',
'(-z+3/4, y+3/4, x+1/4)',
'(-z+3/4, y+1/4, x+3/4)',
'(-z+1/4, y+3/4, x+3/4)',
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'(-z+1/4, -y+1/4, -x+1/4)',
'(-z+1/4, -y+3/4, -x+3/4)',
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'(-x+3/4, -y+1/4, -z+1/4)',
'(-x+1/4, -y+3/4, -z+1/4)',
'(-x+1/4, -y+1/4, -z+3/4)',
'(x+3/4, y+1/4, -z+1/4)',
'(x+3/4, y+3/4, -z+3/4)',
'(x+1/4, y+1/4, -z+3/4)',
'(x+1/4, y+3/4, -z+1/4)',
'(x+1/4, -y+1/4, z+3/4)',
'(x+1/4, -y+3/4, z+1/4)',
'(x+3/4, -y+1/4, z+1/4)',
'(x+3/4, -y+3/4, z+3/4)',
'(-x+1/4, y+3/4, z+1/4)',
'(-x+1/4, y+1/4, z+3/4)',
'(-x+3/4, y+3/4, z+3/4)',
'(-x+3/4, y+1/4, z+1/4)',
'(-z+3/4, -x+3/4, -y+3/4)',
'(-z+3/4, -x+1/4, -y+1/4)',
'(-z+1/4, -x+3/4, -y+1/4)',
'(-z+1/4, -x+1/4, -y+3/4)',
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'(-z+3/4, x+1/4, y+1/4)',
'(z+3/4, x+1/4, -y+1/4)',
'(z+3/4, x+3/4, -y+3/4)',
'(z+1/4, x+1/4, -y+3/4)',
'(z+1/4, x+3/4, -y+1/4)',
'(z+1/4, -x+1/4, y+3/4)',
'(z+1/4, -x+3/4, y+1/4)',
'(z+3/4, -x+1/4, y+1/4)',
'(z+3/4, -x+3/4, y+3/4)',
'(-y+3/4, -z+3/4, -x+3/4)',
'(-y+3/4, -z+1/4, -x+1/4)',
'(-y+1/4, -z+3/4, -x+1/4)',
'(-y+1/4, -z+1/4, -x+3/4)',
'(y+1/4, -z+1/4, x+3/4)',
'(y+1/4, -z+3/4, x+1/4)',
'(y+3/4, -z+1/4, x+1/4)',
'(y+3/4, -z+3/4, x+3/4)',
'(-y+1/4, z+3/4, x+1/4)',
'(-y+1/4, z+1/4, x+3/4)',
'(-y+3/4, z+3/4, x+3/4)',
'(-y+3/4, z+1/4, x+1/4)',
'(y+3/4, z+1/4, -x+1/4)',
'(y+3/4, z+3/4, -x+3/4)',
'(y+1/4, z+1/4, -x+3/4)',
'(y+1/4, z+3/4, -x+1/4)', '(-y, -x+1/2, z)',
'(-y, -x, z+1/2)', '(-y+1/2, -x+1/2, z+1/2)',
'(-y+1/2, -x, z)', '(y+1/2, x+1/2, z+1/2)',
'(y+1/2, x, z)', '(y, x+1/2, z)',
'(y, x, z+1/2)', '(-y+1/2, x, -z)',
'(-y+1/2, x+1/2, -z+1/2)', '(-y, x, -z+1/2)',
'(-y, x+1/2, -z)', '(y, -x, -z+1/2)',
'(y, -x+1/2, -z)', '(y+1/2, -x, -z)',
'(y+1/2, -x+1/2, -z+1/2)', '(-x, -z+1/2, y)',
'(-x, -z, y+1/2)', '(-x+1/2, -z+1/2, y+1/2)',
'(-x+1/2, -z, y)', '(x, -z, -y+1/2)',
'(x, -z+1/2, -y)', '(x+1/2, -z, -y)',
'(x+1/2, -z+1/2, -y+1/2)',
'(x+1/2, z+1/2, y+1/2)', '(x+1/2, z, y)',
'(x, z+1/2, y)', '(x, z, y+1/2)',
'(-x+1/2, z, -y)', '(-x+1/2, z+1/2, -y+1/2)',
'(-x, z, -y+1/2)', '(-x, z+1/2, -y)',
'(-z, -y+1/2, x)', '(-z, -y, x+1/2)',
'(-z+1/2, -y+1/2, x+1/2)', '(-z+1/2, -y, x)',
'(-z+1/2, y, -x)', '(-z+1/2, y+1/2, -x+1/2)',
'(-z, y, -x+1/2)', '(-z, y+1/2, -x)',
'(z, -y, -x+1/2)', '(z, -y+1/2, -x)',
'(z+1/2, -y, -x)', '(z+1/2, -y+1/2, -x+1/2)',
'(z+1/2, y+1/2, x+1/2)', '(z+1/2, y, x)',
'(z, y+1/2, x)', '(z, y, x+1/2)'),
'hkl: h+k=2n, h+l,k+l=2n, 0kl: k+l=4n, k,l=2n, '
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'228:2': {'16a': (0, ('(1/8, 1/8, 1/8)', '(1/8, 5/8, 5/8)',
'(5/8, 1/8, 5/8)', '(5/8, 5/8, 1/8)',
'(7/8, 3/8, 7/8)', '(7/8, 7/8, 3/8)',
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'(7/8, 7/8, 7/8)', '(7/8, 3/8, 3/8)',
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'(1/8, 5/8, 1/8)', '(1/8, 1/8, 5/8)',
'(5/8, 5/8, 5/8)', '(5/8, 1/8, 1/8)'), 'n/a'),
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'(3/4, 1/4, 3/4)', '(3/4, 3/4, 1/4)',
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'(1/4, 1/2, 1/2)', '(3/4, 3/4, 3/4)',
'(3/4, 1/4, 1/4)', '(1/4, 3/4, 1/4)',
'(1/4, 1/4, 3/4)', '(0, 1/2, 1/4)', '(0, 0, 3/4)',
'(1/2, 1/2, 3/4)', '(1/2, 0, 1/4)',
'(1/2, 1/4, 0)', '(1/2, 3/4, 1/2)',
'(0, 1/4, 1/2)', '(0, 3/4, 0)', '(1/4, 0, 1/2)',
'(1/4, 1/2, 0)', '(3/4, 0, 0)', '(3/4, 1/2, 1/2)'
), 'n/a'),
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'(1/2, 1/2, 0)', '(1/4, 3/4, 1/2)',
'(1/4, 1/4, 0)', '(3/4, 3/4, 0)',
'(3/4, 1/4, 1/2)', '(3/4, 1/2, 1/4)',
'(3/4, 0, 3/4)', '(1/4, 1/2, 3/4)',
'(1/4, 0, 1/4)', '(1/2, 1/4, 3/4)',
'(1/2, 3/4, 1/4)', '(0, 1/4, 1/4)',
'(0, 3/4, 3/4)', '(3/4, 1/4, 0)',
'(3/4, 3/4, 1/2)', '(1/4, 1/4, 1/2)',
'(1/4, 3/4, 0)', '(1/2, 1/2, 1/2)', '(1/2, 0, 0)',
'(0, 1/2, 0)', '(0, 0, 1/2)', '(1/4, 0, 3/4)',
'(1/4, 1/2, 1/4)', '(3/4, 0, 1/4)',
'(3/4, 1/2, 3/4)', '(0, 3/4, 1/4)',
'(0, 1/4, 3/4)', '(1/2, 3/4, 3/4)',
'(1/2, 1/4, 1/4)'), 'n/a'),
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'(3/8, 1/8, 5/8)', '(3/8, 5/8, 1/8)',
'(3/8, 5/8, 5/8)', '(3/8, 1/8, 1/8)',
'(7/8, 5/8, 1/8)', '(7/8, 1/8, 5/8)',
'(1/8, 7/8, 1/8)', '(1/8, 3/8, 5/8)',
'(5/8, 7/8, 5/8)', '(5/8, 3/8, 1/8)',
'(5/8, 3/8, 5/8)', '(5/8, 7/8, 1/8)',
'(1/8, 3/8, 1/8)', '(1/8, 7/8, 5/8)',
'(1/8, 1/8, 7/8)', '(1/8, 5/8, 3/8)',
'(5/8, 1/8, 3/8)', '(5/8, 5/8, 7/8)',
'(5/8, 5/8, 3/8)', '(5/8, 1/8, 7/8)',
'(1/8, 5/8, 7/8)', '(1/8, 1/8, 3/8)',
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'(3/8, 7/8, 5/8)', '(3/8, 3/8, 1/8)',
'(7/8, 7/8, 1/8)', '(7/8, 3/8, 5/8)'), 'n/a'),
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'(-x+1/4, -x+3/4, x+1/2)', '(-x+1/4, -x+1/4, x)',
'(-x+3/4, -x+3/4, x)', '(-x+3/4, -x+1/4, x+1/2)',
'(-x+3/4, x+1/2, -x+1/4)', '(-x+3/4, x, -x+3/4)',
'(-x+1/4, x+1/2, -x+3/4)', '(-x+1/4, x, -x+1/4)',
'(x+1/2, -x+1/4, -x+3/4)',
'(x+1/2, -x+3/4, -x+1/4)', '(x, -x+1/4, -x+1/4)',
'(x, -x+3/4, -x+3/4)', '(x+3/4, x+1/4, -x)',
'(x+3/4, x+3/4, -x+1/2)',
'(x+1/4, x+1/4, -x+1/2)', '(x+1/4, x+3/4, -x)',
'(-x+1/2, -x+1/2, -x+1/2)', '(-x+1/2, -x, -x)',
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'(x+1/4, -x, x+3/4)', '(x+1/4, -x+1/2, x+1/4)',
'(x+3/4, -x, x+1/4)', '(x+3/4, -x+1/2, x+3/4)',
'(-x, x+3/4, x+1/4)', '(-x, x+1/4, x+3/4)',
'(-x+1/2, x+3/4, x+3/4)',
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'(-x, -x+1/2, -x+1/2)', '(-x+1/2, -x, -x+1/2)',
'(-x+1/2, -x+1/2, -x)', '(x+3/4, x+1/4, -x+1/2)',
'(x+3/4, x+3/4, -x)', '(x+1/4, x+1/4, -x)',
'(x+1/4, x+3/4, -x+1/2)',
'(x+1/4, -x+1/2, x+3/4)', '(x+1/4, -x, x+1/4)',
'(x+3/4, -x+1/2, x+1/4)', '(x+3/4, -x, x+3/4)',
'(-x+1/2, x+3/4, x+1/4)',
'(-x+1/2, x+1/4, x+3/4)', '(-x, x+3/4, x+3/4)',
'(-x, x+1/4, x+1/4)', '(-x+1/4, -x+3/4, x)',
'(-x+1/4, -x+1/4, x+1/2)',
'(-x+3/4, -x+3/4, x+1/2)', '(-x+3/4, -x+1/4, x)',
'(x+1/2, x+1/2, x+1/2)', '(x+1/2, x, x)',
'(x, x+1/2, x)', '(x, x, x+1/2)',
'(-x+3/4, x, -x+1/4)', '(-x+3/4, x+1/2, -x+3/4)',
'(-x+1/4, x, -x+3/4)', '(-x+1/4, x+1/2, -x+1/4)',
'(x, -x+1/4, -x+3/4)', '(x, -x+3/4, -x+1/4)',
'(x+1/2, -x+1/4, -x+1/4)',
'(x+1/2, -x+3/4, -x+3/4)'), 'n/a'),
'96f': (1, ('(x, 1/8, 1/8)', '(x, 5/8, 5/8)',
'(x+1/2, 1/8, 5/8)', '(x+1/2, 5/8, 1/8)',
'(-x+1/4, 5/8, 5/8)', '(-x+1/4, 1/8, 1/8)',
'(-x+3/4, 5/8, 1/8)', '(-x+3/4, 1/8, 5/8)',
'(1/8, x, 1/8)', '(1/8, x+1/2, 5/8)',
'(5/8, x, 5/8)', '(5/8, x+1/2, 1/8)',
'(5/8, -x+1/4, 5/8)', '(5/8, -x+3/4, 1/8)',
'(1/8, -x+1/4, 1/8)', '(1/8, -x+3/4, 5/8)',
'(1/8, 1/8, x)', '(1/8, 5/8, x+1/2)',
'(5/8, 1/8, x+1/2)', '(5/8, 5/8, x)',
'(5/8, 5/8, -x+1/4)', '(5/8, 1/8, -x+3/4)',
'(1/8, 5/8, -x+3/4)', '(1/8, 1/8, -x+1/4)',
'(7/8, x+1/4, 7/8)', '(7/8, x+3/4, 3/8)',
'(3/8, x+1/4, 3/8)', '(3/8, x+3/4, 7/8)',
'(3/8, -x+1/2, 3/8)', '(3/8, -x, 7/8)',
'(7/8, -x+1/2, 7/8)', '(7/8, -x, 3/8)',
'(x+3/4, 3/8, 7/8)', '(x+3/4, 7/8, 3/8)',
'(x+1/4, 3/8, 3/8)', '(x+1/4, 7/8, 7/8)',
'(-x, 7/8, 3/8)', '(-x, 3/8, 7/8)',
'(-x+1/2, 7/8, 7/8)', '(-x+1/2, 3/8, 3/8)',
'(7/8, 3/8, -x)', '(7/8, 7/8, -x+1/2)',
'(3/8, 3/8, -x+1/2)', '(3/8, 7/8, -x)',
'(3/8, 7/8, x+3/4)', '(3/8, 3/8, x+1/4)',
'(7/8, 7/8, x+1/4)', '(7/8, 3/8, x+3/4)',
'(-x, 7/8, 7/8)', '(-x, 3/8, 3/8)',
'(-x+1/2, 7/8, 3/8)', '(-x+1/2, 3/8, 7/8)',
'(x+3/4, 3/8, 3/8)', '(x+3/4, 7/8, 7/8)',
'(x+1/4, 3/8, 7/8)', '(x+1/4, 7/8, 3/8)',
'(7/8, -x, 7/8)', '(7/8, -x+1/2, 3/8)',
'(3/8, -x, 3/8)', '(3/8, -x+1/2, 7/8)',
'(3/8, x+3/4, 3/8)', '(3/8, x+1/4, 7/8)',
'(7/8, x+3/4, 7/8)', '(7/8, x+1/4, 3/8)',
'(7/8, 7/8, -x)', '(7/8, 3/8, -x+1/2)',
'(3/8, 7/8, -x+1/2)', '(3/8, 3/8, -x)',
'(3/8, 3/8, x+3/4)', '(3/8, 7/8, x+1/4)',
'(7/8, 3/8, x+1/4)', '(7/8, 7/8, x+3/4)',
'(1/8, -x+3/4, 1/8)', '(1/8, -x+1/4, 5/8)',
'(5/8, -x+3/4, 5/8)', '(5/8, -x+1/4, 1/8)',
'(5/8, x+1/2, 5/8)', '(5/8, x, 1/8)',
'(1/8, x+1/2, 1/8)', '(1/8, x, 5/8)',
'(-x+1/4, 5/8, 1/8)', '(-x+1/4, 1/8, 5/8)',
'(-x+3/4, 5/8, 5/8)', '(-x+3/4, 1/8, 1/8)',
'(x, 1/8, 5/8)', '(x, 5/8, 1/8)',
'(x+1/2, 1/8, 1/8)', '(x+1/2, 5/8, 5/8)',
'(1/8, 5/8, x)', '(1/8, 1/8, x+1/2)',
'(5/8, 5/8, x+1/2)', '(5/8, 1/8, x)',
'(5/8, 1/8, -x+1/4)', '(5/8, 5/8, -x+3/4)',
'(1/8, 1/8, -x+3/4)', '(1/8, 5/8, -x+1/4)'), 'n/a'
),
'96g': (2, ('(1/4, y, -y)', '(1/4, y+1/2, -y+1/2)',
'(3/4, y, -y+1/2)', '(3/4, y+1/2, -y)',
'(0, -y+3/4, -y+1/2)', '(0, -y+1/4, -y)',
'(1/2, -y+3/4, -y)', '(1/2, -y+1/4, -y+1/2)',
'(1/2, y+1/2, y+1/4)', '(1/2, y, y+3/4)',
'(0, y+1/2, y+3/4)', '(0, y, y+1/4)',
'(3/4, -y+1/4, y+3/4)', '(3/4, -y+3/4, y+1/4)',
'(1/4, -y+1/4, y+1/4)', '(1/4, -y+3/4, y+3/4)',
'(-y, 1/4, y)', '(-y, 3/4, y+1/2)',
'(-y+1/2, 1/4, y+1/2)', '(-y+1/2, 3/4, y)',
'(-y+1/2, 0, -y+3/4)', '(-y+1/2, 1/2, -y+1/4)',
'(-y, 0, -y+1/4)', '(-y, 1/2, -y+3/4)',
'(y+1/4, 1/2, y+1/2)', '(y+1/4, 0, y)',
'(y+3/4, 1/2, y)', '(y+3/4, 0, y+1/2)',
'(y+3/4, 3/4, -y+1/4)', '(y+3/4, 1/4, -y+3/4)',
'(y+1/4, 3/4, -y+3/4)', '(y+1/4, 1/4, -y+1/4)',
'(y, -y, 1/4)', '(y, -y+1/2, 3/4)',
'(y+1/2, -y, 3/4)', '(y+1/2, -y+1/2, 1/4)',
'(-y+3/4, -y+1/2, 0)', '(-y+3/4, -y, 1/2)',
'(-y+1/4, -y+1/2, 1/2)', '(-y+1/4, -y, 0)',
'(y+1/2, y+1/4, 1/2)', '(y+1/2, y+3/4, 0)',
'(y, y+1/4, 0)', '(y, y+3/4, 1/2)',
'(-y+1/4, y+3/4, 3/4)', '(-y+1/4, y+1/4, 1/4)',
'(-y+3/4, y+3/4, 1/4)', '(-y+3/4, y+1/4, 3/4)',
'(3/4, -y, y)', '(3/4, -y+1/2, y+1/2)',
'(1/4, -y, y+1/2)', '(1/4, -y+1/2, y)',
'(0, y+1/4, y+1/2)', '(0, y+3/4, y)',
'(1/2, y+1/4, y)', '(1/2, y+3/4, y+1/2)',
'(1/2, -y+1/2, -y+3/4)', '(1/2, -y, -y+1/4)',
'(0, -y+1/2, -y+1/4)', '(0, -y, -y+3/4)',
'(1/4, y+3/4, -y+1/4)', '(1/4, y+1/4, -y+3/4)',
'(3/4, y+3/4, -y+3/4)', '(3/4, y+1/4, -y+1/4)',
'(y, 3/4, -y)', '(y, 1/4, -y+1/2)',
'(y+1/2, 3/4, -y+1/2)', '(y+1/2, 1/4, -y)',
'(y+1/2, 0, y+1/4)', '(y+1/2, 1/2, y+3/4)',
'(y, 0, y+3/4)', '(y, 1/2, y+1/4)',
'(-y+3/4, 1/2, -y+1/2)', '(-y+3/4, 0, -y)',
'(-y+1/4, 1/2, -y)', '(-y+1/4, 0, -y+1/2)',
'(-y+1/4, 1/4, y+3/4)', '(-y+1/4, 3/4, y+1/4)',
'(-y+3/4, 1/4, y+1/4)', '(-y+3/4, 3/4, y+3/4)',
'(-y, y, 3/4)', '(-y, y+1/2, 1/4)',
'(-y+1/2, y, 1/4)', '(-y+1/2, y+1/2, 3/4)',
'(y+1/4, y+1/2, 0)', '(y+1/4, y, 1/2)',
'(y+3/4, y+1/2, 1/2)', '(y+3/4, y, 0)',
'(-y+1/2, -y+3/4, 1/2)', '(-y+1/2, -y+1/4, 0)',
'(-y, -y+3/4, 0)', '(-y, -y+1/4, 1/2)',
'(y+3/4, -y+1/4, 1/4)', '(y+3/4, -y+3/4, 3/4)',
'(y+1/4, -y+1/4, 3/4)', '(y+1/4, -y+3/4, 1/4)'),
'n/a'),
'192h': (7, ('(x, y, z)', '(x, y+1/2, z+1/2)',
'(x+1/2, y, z+1/2)', '(x+1/2, y+1/2, z)',
'(-x+1/4, -y+3/4, z+1/2)', '(-x+1/4, -y+1/4, z)',
'(-x+3/4, -y+3/4, z)', '(-x+3/4, -y+1/4, z+1/2)',
'(-x+3/4, y+1/2, -z+1/4)', '(-x+3/4, y, -z+3/4)',
'(-x+1/4, y+1/2, -z+3/4)', '(-x+1/4, y, -z+1/4)',
'(x+1/2, -y+1/4, -z+3/4)',
'(x+1/2, -y+3/4, -z+1/4)', '(x, -y+1/4, -z+1/4)',
'(x, -y+3/4, -z+3/4)', '(z, x, y)',
'(z, x+1/2, y+1/2)', '(z+1/2, x, y+1/2)',
'(z+1/2, x+1/2, y)', '(z+1/2, -x+1/4, -y+3/4)',
'(z+1/2, -x+3/4, -y+1/4)', '(z, -x+1/4, -y+1/4)',
'(z, -x+3/4, -y+3/4)', '(-z+1/4, -x+3/4, y+1/2)',
'(-z+1/4, -x+1/4, y)', '(-z+3/4, -x+3/4, y)',
'(-z+3/4, -x+1/4, y+1/2)',
'(-z+3/4, x+1/2, -y+1/4)', '(-z+3/4, x, -y+3/4)',
'(-z+1/4, x+1/2, -y+3/4)', '(-z+1/4, x, -y+1/4)',
'(y, z, x)', '(y, z+1/2, x+1/2)',
'(y+1/2, z, x+1/2)', '(y+1/2, z+1/2, x)',
'(-y+3/4, z+1/2, -x+1/4)', '(-y+3/4, z, -x+3/4)',
'(-y+1/4, z+1/2, -x+3/4)', '(-y+1/4, z, -x+1/4)',
'(y+1/2, -z+1/4, -x+3/4)',
'(y+1/2, -z+3/4, -x+1/4)', '(y, -z+1/4, -x+1/4)',
'(y, -z+3/4, -x+3/4)', '(-y+1/4, -z+3/4, x+1/2)',
'(-y+1/4, -z+1/4, x)', '(-y+3/4, -z+3/4, x)',
'(-y+3/4, -z+1/4, x+1/2)', '(y+3/4, x+1/4, -z)',
'(y+3/4, x+3/4, -z+1/2)',
'(y+1/4, x+1/4, -z+1/2)', '(y+1/4, x+3/4, -z)',
'(-y+1/2, -x+1/2, -z+1/2)', '(-y+1/2, -x, -z)',
'(-y, -x+1/2, -z)', '(-y, -x, -z+1/2)',
'(y+1/4, -x, z+3/4)', '(y+1/4, -x+1/2, z+1/4)',
'(y+3/4, -x, z+1/4)', '(y+3/4, -x+1/2, z+3/4)',
'(-y, x+3/4, z+1/4)', '(-y, x+1/4, z+3/4)',
'(-y+1/2, x+3/4, z+3/4)',
'(-y+1/2, x+1/4, z+1/4)', '(x+3/4, z+1/4, -y)',
'(x+3/4, z+3/4, -y+1/2)',
'(x+1/4, z+1/4, -y+1/2)', '(x+1/4, z+3/4, -y)',
'(-x, z+3/4, y+1/4)', '(-x, z+1/4, y+3/4)',
'(-x+1/2, z+3/4, y+3/4)',
'(-x+1/2, z+1/4, y+1/4)',
'(-x+1/2, -z+1/2, -y+1/2)', '(-x+1/2, -z, -y)',
'(-x, -z+1/2, -y)', '(-x, -z, -y+1/2)',
'(x+1/4, -z, y+3/4)', '(x+1/4, -z+1/2, y+1/4)',
'(x+3/4, -z, y+1/4)', '(x+3/4, -z+1/2, y+3/4)',
'(z+3/4, y+1/4, -x)', '(z+3/4, y+3/4, -x+1/2)',
'(z+1/4, y+1/4, -x+1/2)', '(z+1/4, y+3/4, -x)',
'(z+1/4, -y, x+3/4)', '(z+1/4, -y+1/2, x+1/4)',
'(z+3/4, -y, x+1/4)', '(z+3/4, -y+1/2, x+3/4)',
'(-z, y+3/4, x+1/4)', '(-z, y+1/4, x+3/4)',
'(-z+1/2, y+3/4, x+3/4)',
'(-z+1/2, y+1/4, x+1/4)',
'(-z+1/2, -y+1/2, -x+1/2)', '(-z+1/2, -y, -x)',
'(-z, -y+1/2, -x)', '(-z, -y, -x+1/2)',
'(-x, -y, -z)', '(-x, -y+1/2, -z+1/2)',
'(-x+1/2, -y, -z+1/2)', '(-x+1/2, -y+1/2, -z)',
'(x+3/4, y+1/4, -z+1/2)', '(x+3/4, y+3/4, -z)',
'(x+1/4, y+1/4, -z)', '(x+1/4, y+3/4, -z+1/2)',
'(x+1/4, -y+1/2, z+3/4)', '(x+1/4, -y, z+1/4)',
'(x+3/4, -y+1/2, z+1/4)', '(x+3/4, -y, z+3/4)',
'(-x+1/2, y+3/4, z+1/4)',
'(-x+1/2, y+1/4, z+3/4)', '(-x, y+3/4, z+3/4)',
'(-x, y+1/4, z+1/4)', '(-z, -x, -y)',
'(-z, -x+1/2, -y+1/2)', '(-z+1/2, -x, -y+1/2)',
'(-z+1/2, -x+1/2, -y)', '(-z+1/2, x+3/4, y+1/4)',
'(-z+1/2, x+1/4, y+3/4)', '(-z, x+3/4, y+3/4)',
'(-z, x+1/4, y+1/4)', '(z+3/4, x+1/4, -y+1/2)',
'(z+3/4, x+3/4, -y)', '(z+1/4, x+1/4, -y)',
'(z+1/4, x+3/4, -y+1/2)',
'(z+1/4, -x+1/2, y+3/4)', '(z+1/4, -x, y+1/4)',
'(z+3/4, -x+1/2, y+1/4)', '(z+3/4, -x, y+3/4)',
'(-y, -z, -x)', '(-y, -z+1/2, -x+1/2)',
'(-y+1/2, -z, -x+1/2)', '(-y+1/2, -z+1/2, -x)',
'(y+1/4, -z+1/2, x+3/4)', '(y+1/4, -z, x+1/4)',
'(y+3/4, -z+1/2, x+1/4)', '(y+3/4, -z, x+3/4)',
'(-y+1/2, z+3/4, x+1/4)',
'(-y+1/2, z+1/4, x+3/4)', '(-y, z+3/4, x+3/4)',
'(-y, z+1/4, x+1/4)', '(y+3/4, z+1/4, -x+1/2)',
'(y+3/4, z+3/4, -x)', '(y+1/4, z+1/4, -x)',
'(y+1/4, z+3/4, -x+1/2)', '(-y+1/4, -x+3/4, z)',
'(-y+1/4, -x+1/4, z+1/2)',
'(-y+3/4, -x+3/4, z+1/2)', '(-y+3/4, -x+1/4, z)',
'(y+1/2, x+1/2, z+1/2)', '(y+1/2, x, z)',
'(y, x+1/2, z)', '(y, x, z+1/2)',
'(-y+3/4, x, -z+1/4)', '(-y+3/4, x+1/2, -z+3/4)',
'(-y+1/4, x, -z+3/4)', '(-y+1/4, x+1/2, -z+1/4)',
'(y, -x+1/4, -z+3/4)', '(y, -x+3/4, -z+1/4)',
'(y+1/2, -x+1/4, -z+1/4)',
'(y+1/2, -x+3/4, -z+3/4)', '(-x+1/4, -z+3/4, y)',
'(-x+1/4, -z+1/4, y+1/2)',
'(-x+3/4, -z+3/4, y+1/2)', '(-x+3/4, -z+1/4, y)',
'(x, -z+1/4, -y+3/4)', '(x, -z+3/4, -y+1/4)',
'(x+1/2, -z+1/4, -y+1/4)',
'(x+1/2, -z+3/4, -y+3/4)',
'(x+1/2, z+1/2, y+1/2)', '(x+1/2, z, y)',
'(x, z+1/2, y)', '(x, z, y+1/2)',
'(-x+3/4, z, -y+1/4)', '(-x+3/4, z+1/2, -y+3/4)',
'(-x+1/4, z, -y+3/4)', '(-x+1/4, z+1/2, -y+1/4)',
'(-z+1/4, -y+3/4, x)', '(-z+1/4, -y+1/4, x+1/2)',
'(-z+3/4, -y+3/4, x+1/2)', '(-z+3/4, -y+1/4, x)',
'(-z+3/4, y, -x+1/4)', '(-z+3/4, y+1/2, -x+3/4)',
'(-z+1/4, y, -x+3/4)', '(-z+1/4, y+1/2, -x+1/4)',
'(z, -y+1/4, -x+3/4)', '(z, -y+3/4, -x+1/4)',
'(z+1/2, -y+1/4, -x+1/4)',
'(z+1/2, -y+3/4, -x+3/4)',
'(z+1/2, y+1/2, x+1/2)', '(z+1/2, y, x)',
'(z, y+1/2, x)', '(z, y, x+1/2)'), 'n/a')},
'229': {'2a': (0, ('(0, 0, 0)', '(1/2, 1/2, 1/2)'), None),
'6b': (0, ('(0, 1/2, 1/2)', '(1/2, 0, 0)', '(1/2, 0, 1/2)',
'(0, 1/2, 0)', '(1/2, 1/2, 0)', '(0, 0, 1/2)'), None
),
'8c': (0, ('(1/4, 1/4, 1/4)', '(3/4, 3/4, 3/4)',
'(3/4, 3/4, 1/4)', '(1/4, 1/4, 3/4)',
'(3/4, 1/4, 3/4)', '(1/4, 3/4, 1/4)',
'(1/4, 3/4, 3/4)', '(3/4, 1/4, 1/4)'), 'hkl: k,l=2n'
),
'12d': (0, ('(1/4, 0, 1/2)', '(3/4, 1/2, 0)', '(3/4, 0, 1/2)',
'(1/4, 1/2, 0)', '(1/2, 1/4, 0)', '(0, 3/4, 1/2)',
'(1/2, 3/4, 0)', '(0, 1/4, 1/2)', '(0, 1/2, 1/4)',
'(1/2, 0, 3/4)', '(0, 1/2, 3/4)', '(1/2, 0, 1/4)'),
None),
'12e': (1, ('(x, 0, 0)', '(x+1/2, 1/2, 1/2)', '(-x, 0, 0)',
'(-x+1/2, 1/2, 1/2)', '(0, x, 0)',
'(1/2, x+1/2, 1/2)', '(0, -x, 0)',
'(1/2, -x+1/2, 1/2)', '(0, 0, x)',
'(1/2, 1/2, x+1/2)', '(0, 0, -x)',
'(1/2, 1/2, -x+1/2)'), None),
'16f': (1, ('(x, x, x)', '(x+1/2, x+1/2, x+1/2)', '(-x, -x, x)',
'(-x+1/2, -x+1/2, x+1/2)', '(-x, x, -x)',
'(-x+1/2, x+1/2, -x+1/2)', '(x, -x, -x)',
'(x+1/2, -x+1/2, -x+1/2)', '(x, x, -x)',
'(x+1/2, x+1/2, -x+1/2)', '(-x, -x, -x)',
'(-x+1/2, -x+1/2, -x+1/2)', '(x, -x, x)',
'(x+1/2, -x+1/2, x+1/2)', '(-x, x, x)',
'(-x+1/2, x+1/2, x+1/2)'), None),
'24g': (1, ('(x, 0, 1/2)', '(x+1/2, 1/2, 0)', '(-x, 0, 1/2)',
'(-x+1/2, 1/2, 0)', '(1/2, x, 0)',
'(0, x+1/2, 1/2)', '(1/2, -x, 0)',
'(0, -x+1/2, 1/2)', '(0, 1/2, x)',
'(1/2, 0, x+1/2)', '(0, 1/2, -x)',
'(1/2, 0, -x+1/2)', '(0, x, 1/2)',
'(1/2, x+1/2, 0)', '(0, -x, 1/2)',
'(1/2, -x+1/2, 0)', '(x, 1/2, 0)',
'(x+1/2, 0, 1/2)', '(-x, 1/2, 0)',
'(-x+1/2, 0, 1/2)', '(1/2, 0, -x)',
'(0, 1/2, -x+1/2)', '(1/2, 0, x)',
'(0, 1/2, x+1/2)'), None),
'24h': (2, ('(0, y, y)', '(1/2, y+1/2, y+1/2)', '(0, -y, y)',
'(1/2, -y+1/2, y+1/2)', '(0, y, -y)',
'(1/2, y+1/2, -y+1/2)', '(0, -y, -y)',
'(1/2, -y+1/2, -y+1/2)', '(y, 0, y)',
'(y+1/2, 1/2, y+1/2)', '(y, 0, -y)',
'(y+1/2, 1/2, -y+1/2)', '(-y, 0, y)',
'(-y+1/2, 1/2, y+1/2)', '(-y, 0, -y)',
'(-y+1/2, 1/2, -y+1/2)', '(y, y, 0)',
'(y+1/2, y+1/2, 1/2)', '(-y, y, 0)',
'(-y+1/2, y+1/2, 1/2)', '(y, -y, 0)',
'(y+1/2, -y+1/2, 1/2)', '(-y, -y, 0)',
'(-y+1/2, -y+1/2, 1/2)'), None),
'48i': (2, ('(1/4, y, -y+1/2)', '(3/4, y+1/2, -y)',
'(3/4, -y, -y+1/2)', '(1/4, -y+1/2, -y)',
'(3/4, y, y+1/2)', '(1/4, y+1/2, y)',
'(1/4, -y, y+1/2)', '(3/4, -y+1/2, y)',
'(-y+1/2, 1/4, y)', '(-y, 3/4, y+1/2)',
'(-y+1/2, 3/4, -y)', '(-y, 1/4, -y+1/2)',
'(y+1/2, 3/4, y)', '(y, 1/4, y+1/2)',
'(y+1/2, 1/4, -y)', '(y, 3/4, -y+1/2)',
'(y, -y+1/2, 1/4)', '(y+1/2, -y, 3/4)',
'(-y, -y+1/2, 3/4)', '(-y+1/2, -y, 1/4)',
'(y, y+1/2, 3/4)', '(y+1/2, y, 1/4)',
'(-y, y+1/2, 1/4)', '(-y+1/2, y, 3/4)',
'(3/4, -y, y+1/2)', '(1/4, -y+1/2, y)',
'(1/4, y, y+1/2)', '(3/4, y+1/2, y)',
'(1/4, -y, -y+1/2)', '(3/4, -y+1/2, -y)',
'(3/4, y, -y+1/2)', '(1/4, y+1/2, -y)',
'(y+1/2, 3/4, -y)', '(y, 1/4, -y+1/2)',
'(y+1/2, 1/4, y)', '(y, 3/4, y+1/2)',
'(-y+1/2, 1/4, -y)', '(-y, 3/4, -y+1/2)',
'(-y+1/2, 3/4, y)', '(-y, 1/4, y+1/2)',
'(-y, y+1/2, 3/4)', '(-y+1/2, y, 1/4)',
'(y, y+1/2, 1/4)', '(y+1/2, y, 3/4)',
'(-y, -y+1/2, 1/4)', '(-y+1/2, -y, 3/4)',
'(y, -y+1/2, 3/4)', '(y+1/2, -y, 1/4)'), None),
'48j': (6, ('(0, y, z)', '(1/2, y+1/2, z+1/2)', '(0, -y, z)',
'(1/2, -y+1/2, z+1/2)', '(0, y, -z)',
'(1/2, y+1/2, -z+1/2)', '(0, -y, -z)',
'(1/2, -y+1/2, -z+1/2)', '(z, 0, y)',
'(z+1/2, 1/2, y+1/2)', '(z, 0, -y)',
'(z+1/2, 1/2, -y+1/2)', '(-z, 0, y)',
'(-z+1/2, 1/2, y+1/2)', '(-z, 0, -y)',
'(-z+1/2, 1/2, -y+1/2)', '(y, z, 0)',
'(y+1/2, z+1/2, 1/2)', '(-y, z, 0)',
'(-y+1/2, z+1/2, 1/2)', '(y, -z, 0)',
'(y+1/2, -z+1/2, 1/2)', '(-y, -z, 0)',
'(-y+1/2, -z+1/2, 1/2)', '(y, 0, -z)',
'(y+1/2, 1/2, -z+1/2)', '(-y, 0, -z)',
'(-y+1/2, 1/2, -z+1/2)', '(y, 0, z)',
'(y+1/2, 1/2, z+1/2)', '(-y, 0, z)',
'(-y+1/2, 1/2, z+1/2)', '(0, z, -y)',
'(1/2, z+1/2, -y+1/2)', '(0, z, y)',
'(1/2, z+1/2, y+1/2)', '(0, -z, -y)',
'(1/2, -z+1/2, -y+1/2)', '(0, -z, y)',
'(1/2, -z+1/2, y+1/2)', '(z, y, 0)',
'(z+1/2, y+1/2, 1/2)', '(z, -y, 0)',
'(z+1/2, -y+1/2, 1/2)', '(-z, y, 0)',
'(-z+1/2, y+1/2, 1/2)', '(-z, -y, 0)',
'(-z+1/2, -y+1/2, 1/2)'), None),
'48k': (5, ('(x, x, z)', '(x+1/2, x+1/2, z+1/2)', '(-x, -x, z)',
'(-x+1/2, -x+1/2, z+1/2)', '(-x, x, -z)',
'(-x+1/2, x+1/2, -z+1/2)', '(x, -x, -z)',
'(x+1/2, -x+1/2, -z+1/2)', '(z, x, x)',
'(z+1/2, x+1/2, x+1/2)', '(z, -x, -x)',
'(z+1/2, -x+1/2, -x+1/2)', '(-z, -x, x)',
'(-z+1/2, -x+1/2, x+1/2)', '(-z, x, -x)',
'(-z+1/2, x+1/2, -x+1/2)', '(x, z, x)',
'(x+1/2, z+1/2, x+1/2)', '(-x, z, -x)',
'(-x+1/2, z+1/2, -x+1/2)', '(x, -z, -x)',
'(x+1/2, -z+1/2, -x+1/2)', '(-x, -z, x)',
'(-x+1/2, -z+1/2, x+1/2)', '(x, x, -z)',
'(x+1/2, x+1/2, -z+1/2)', '(-x, -x, -z)',
'(-x+1/2, -x+1/2, -z+1/2)', '(x, -x, z)',
'(x+1/2, -x+1/2, z+1/2)', '(-x, x, z)',
'(-x+1/2, x+1/2, z+1/2)', '(x, z, -x)',
'(x+1/2, z+1/2, -x+1/2)', '(-x, z, x)',
'(-x+1/2, z+1/2, x+1/2)', '(-x, -z, -x)',
'(-x+1/2, -z+1/2, -x+1/2)', '(x, -z, x)',
'(x+1/2, -z+1/2, x+1/2)', '(z, x, -x)',
'(z+1/2, x+1/2, -x+1/2)', '(z, -x, x)',
'(z+1/2, -x+1/2, x+1/2)', '(-z, x, x)',
'(-z+1/2, x+1/2, x+1/2)', '(-z, -x, -x)',
'(-z+1/2, -x+1/2, -x+1/2)'), None),
'96l': (7, ('(x, y, z)', '(x+1/2, y+1/2, z+1/2)', '(-x, -y, z)',
'(-x+1/2, -y+1/2, z+1/2)', '(-x, y, -z)',
'(-x+1/2, y+1/2, -z+1/2)', '(x, -y, -z)',
'(x+1/2, -y+1/2, -z+1/2)', '(z, x, y)',
'(z+1/2, x+1/2, y+1/2)', '(z, -x, -y)',
'(z+1/2, -x+1/2, -y+1/2)', '(-z, -x, y)',
'(-z+1/2, -x+1/2, y+1/2)', '(-z, x, -y)',
'(-z+1/2, x+1/2, -y+1/2)', '(y, z, x)',
'(y+1/2, z+1/2, x+1/2)', '(-y, z, -x)',
'(-y+1/2, z+1/2, -x+1/2)', '(y, -z, -x)',
'(y+1/2, -z+1/2, -x+1/2)', '(-y, -z, x)',
'(-y+1/2, -z+1/2, x+1/2)', '(y, x, -z)',
'(y+1/2, x+1/2, -z+1/2)', '(-y, -x, -z)',
'(-y+1/2, -x+1/2, -z+1/2)', '(y, -x, z)',
'(y+1/2, -x+1/2, z+1/2)', '(-y, x, z)',
'(-y+1/2, x+1/2, z+1/2)', '(x, z, -y)',
'(x+1/2, z+1/2, -y+1/2)', '(-x, z, y)',
'(-x+1/2, z+1/2, y+1/2)', '(-x, -z, -y)',
'(-x+1/2, -z+1/2, -y+1/2)', '(x, -z, y)',
'(x+1/2, -z+1/2, y+1/2)', '(z, y, -x)',
'(z+1/2, y+1/2, -x+1/2)', '(z, -y, x)',
'(z+1/2, -y+1/2, x+1/2)', '(-z, y, x)',
'(-z+1/2, y+1/2, x+1/2)', '(-z, -y, -x)',
'(-z+1/2, -y+1/2, -x+1/2)', '(-x, -y, -z)',
'(-x+1/2, -y+1/2, -z+1/2)', '(x, y, -z)',
'(x+1/2, y+1/2, -z+1/2)', '(x, -y, z)',
'(x+1/2, -y+1/2, z+1/2)', '(-x, y, z)',
'(-x+1/2, y+1/2, z+1/2)', '(-z, -x, -y)',
'(-z+1/2, -x+1/2, -y+1/2)', '(-z, x, y)',
'(-z+1/2, x+1/2, y+1/2)', '(z, x, -y)',
'(z+1/2, x+1/2, -y+1/2)', '(z, -x, y)',
'(z+1/2, -x+1/2, y+1/2)', '(-y, -z, -x)',
'(-y+1/2, -z+1/2, -x+1/2)', '(y, -z, x)',
'(y+1/2, -z+1/2, x+1/2)', '(-y, z, x)',
'(-y+1/2, z+1/2, x+1/2)', '(y, z, -x)',
'(y+1/2, z+1/2, -x+1/2)', '(-y, -x, z)',
'(-y+1/2, -x+1/2, z+1/2)', '(y, x, z)',
'(y+1/2, x+1/2, z+1/2)', '(-y, x, -z)',
'(-y+1/2, x+1/2, -z+1/2)', '(y, -x, -z)',
'(y+1/2, -x+1/2, -z+1/2)', '(-x, -z, y)',
'(-x+1/2, -z+1/2, y+1/2)', '(x, -z, -y)',
'(x+1/2, -z+1/2, -y+1/2)', '(x, z, y)',
'(x+1/2, z+1/2, y+1/2)', '(-x, z, -y)',
'(-x+1/2, z+1/2, -y+1/2)', '(-z, -y, x)',
'(-z+1/2, -y+1/2, x+1/2)', '(-z, y, -x)',
'(-z+1/2, y+1/2, -x+1/2)', '(z, -y, -x)',
'(z+1/2, -y+1/2, -x+1/2)', '(z, y, x)',
'(z+1/2, y+1/2, x+1/2)'),
'hkl: h+k+l=2n, 0kl: k+l=2n, hhl: l=2n, h00: h=2n')},
'230': {'16a': (0, ('(0, 0, 0)', '(1/2, 1/2, 1/2)', '(1/2, 0, 1/2)',
'(0, 1/2, 0)', '(0, 1/2, 1/2)', '(1/2, 0, 0)',
'(1/2, 1/2, 0)', '(0, 0, 1/2)', '(3/4, 1/4, 1/4)',
'(1/4, 3/4, 3/4)', '(3/4, 3/4, 3/4)',
'(1/4, 1/4, 1/4)', '(1/4, 1/4, 3/4)',
'(3/4, 3/4, 1/4)', '(1/4, 3/4, 1/4)',
'(3/4, 1/4, 3/4)'), 'hkl: h,k=2n, h+k+l=4n'),
'16b': (0, ('(1/8, 1/8, 1/8)', '(5/8, 5/8, 5/8)',
'(3/8, 7/8, 5/8)', '(7/8, 3/8, 1/8)',
'(7/8, 5/8, 3/8)', '(3/8, 1/8, 7/8)',
'(5/8, 3/8, 7/8)', '(1/8, 7/8, 3/8)',
'(7/8, 7/8, 7/8)', '(3/8, 3/8, 3/8)',
'(5/8, 1/8, 3/8)', '(1/8, 5/8, 7/8)',
'(1/8, 3/8, 5/8)', '(5/8, 7/8, 1/8)',
'(3/8, 5/8, 1/8)', '(7/8, 1/8, 5/8)'),
'hkl: h,k=2n+1, l=4n+2 or h,k,l=4n'),
'24c': (0, ('(1/8, 0, 1/4)', '(5/8, 1/2, 3/4)', '(3/8, 0, 3/4)',
'(7/8, 1/2, 1/4)', '(1/4, 1/8, 0)',
'(3/4, 5/8, 1/2)', '(3/4, 3/8, 0)',
'(1/4, 7/8, 1/2)', '(0, 1/4, 1/8)',
'(1/2, 3/4, 5/8)', '(0, 3/4, 3/8)',
'(1/2, 1/4, 7/8)', '(7/8, 0, 3/4)',
'(3/8, 1/2, 1/4)', '(5/8, 0, 1/4)',
'(1/8, 1/2, 3/4)', '(3/4, 7/8, 0)',
'(1/4, 3/8, 1/2)', '(1/4, 5/8, 0)',
'(3/4, 1/8, 1/2)', '(0, 3/4, 7/8)',
'(1/2, 1/4, 3/8)', '(0, 1/4, 5/8)',
'(1/2, 3/4, 1/8)'),
'hkl: h,k=2n, h+k+l=4n or h,k=2n+1, '
'l=4n+2 or h=8n, k=8n+4, h+k+l=4n+2'),
'24d': (0, ('(3/8, 0, 1/4)', '(7/8, 1/2, 3/4)', '(1/8, 0, 3/4)',
'(5/8, 1/2, 1/4)', '(1/4, 3/8, 0)',
'(3/4, 7/8, 1/2)', '(3/4, 1/8, 0)',
'(1/4, 5/8, 1/2)', '(0, 1/4, 3/8)',
'(1/2, 3/4, 7/8)', '(0, 3/4, 1/8)',
'(1/2, 1/4, 5/8)', '(3/4, 5/8, 0)',
'(1/4, 1/8, 1/2)', '(3/4, 3/8, 1/2)',
'(1/4, 7/8, 0)', '(1/8, 1/2, 1/4)', '(5/8, 0, 3/4)',
'(7/8, 0, 1/4)', '(3/8, 1/2, 3/4)', '(0, 1/4, 7/8)',
'(1/2, 3/4, 3/8)', '(1/2, 1/4, 1/8)',
'(0, 3/4, 5/8)'),
'hkl: h,k=2n, h+k+l=4n or h,k=2n+1, '
'l=4n+2 or h=8n, k=8n+4, h+k+l=4n+2'),
'32e': (1, ('(x, x, x)', '(x+1/2, x+1/2, x+1/2)',
'(-x+1/2, -x, x+1/2)', '(-x, -x+1/2, x)',
'(-x, x+1/2, -x+1/2)', '(-x+1/2, x, -x)',
'(x+1/2, -x+1/2, -x)', '(x, -x, -x+1/2)',
'(x+3/4, x+1/4, -x+1/4)', '(x+1/4, x+3/4, -x+3/4)',
'(-x+3/4, -x+3/4, -x+3/4)',
'(-x+1/4, -x+1/4, -x+1/4)',
'(x+1/4, -x+1/4, x+3/4)', '(x+3/4, -x+3/4, x+1/4)',
'(-x+1/4, x+3/4, x+1/4)', '(-x+3/4, x+1/4, x+3/4)',
'(-x, -x, -x)', '(-x+1/2, -x+1/2, -x+1/2)',
'(x+1/2, x, -x+1/2)', '(x, x+1/2, -x)',
'(x, -x+1/2, x+1/2)', '(x+1/2, -x, x)',
'(-x+1/2, x+1/2, x)', '(-x, x, x+1/2)',
'(-x+1/4, -x+3/4, x+3/4)',
'(-x+3/4, -x+1/4, x+1/4)', '(x+1/4, x+1/4, x+1/4)',
'(x+3/4, x+3/4, x+3/4)', '(-x+3/4, x+3/4, -x+1/4)',
'(-x+1/4, x+1/4, -x+3/4)',
'(x+3/4, -x+1/4, -x+3/4)',
'(x+1/4, -x+3/4, -x+1/4)'), 'hkl: h=2n+1 or h+k+l=4n'
),
'48f': (1, ('(x, 0, 1/4)', '(x+1/2, 1/2, 3/4)',
'(-x+1/2, 0, 3/4)', '(-x, 1/2, 1/4)', '(1/4, x, 0)',
'(3/4, x+1/2, 1/2)', '(3/4, -x+1/2, 0)',
'(1/4, -x, 1/2)', '(0, 1/4, x)',
'(1/2, 3/4, x+1/2)', '(0, 3/4, -x+1/2)',
'(1/2, 1/4, -x)', '(3/4, x+1/4, 0)',
'(1/4, x+3/4, 1/2)', '(3/4, -x+3/4, 1/2)',
'(1/4, -x+1/4, 0)', '(x+3/4, 1/2, 1/4)',
'(x+1/4, 0, 3/4)', '(-x+1/4, 0, 1/4)',
'(-x+3/4, 1/2, 3/4)', '(0, 1/4, -x+1/4)',
'(1/2, 3/4, -x+3/4)', '(1/2, 1/4, x+3/4)',
'(0, 3/4, x+1/4)', '(-x, 0, 3/4)',
'(-x+1/2, 1/2, 1/4)', '(x+1/2, 0, 1/4)',
'(x, 1/2, 3/4)', '(3/4, -x, 0)',
'(1/4, -x+1/2, 1/2)', '(1/4, x+1/2, 0)',
'(3/4, x, 1/2)', '(0, 3/4, -x)',
'(1/2, 1/4, -x+1/2)', '(0, 1/4, x+1/2)',
'(1/2, 3/4, x)', '(1/4, -x+3/4, 0)',
'(3/4, -x+1/4, 1/2)', '(1/4, x+1/4, 1/2)',
'(3/4, x+3/4, 0)', '(-x+1/4, 1/2, 3/4)',
'(-x+3/4, 0, 1/4)', '(x+3/4, 0, 3/4)',
'(x+1/4, 1/2, 1/4)', '(0, 3/4, x+3/4)',
'(1/2, 1/4, x+1/4)', '(1/2, 3/4, -x+1/4)',
'(0, 1/4, -x+3/4)'), 'hkl: 2h+l=4n'),
'48g': (2, ('(1/8, y, -y+1/4)', '(5/8, y+1/2, -y+3/4)',
'(3/8, -y, -y+3/4)', '(7/8, -y+1/2, -y+1/4)',
'(7/8, y+1/2, y+1/4)', '(3/8, y, y+3/4)',
'(5/8, -y+1/2, y+3/4)', '(1/8, -y, y+1/4)',
'(-y+1/4, 1/8, y)', '(-y+3/4, 5/8, y+1/2)',
'(-y+3/4, 3/8, -y)', '(-y+1/4, 7/8, -y+1/2)',
'(y+1/4, 7/8, y+1/2)', '(y+3/4, 3/8, y)',
'(y+3/4, 5/8, -y+1/2)', '(y+1/4, 1/8, -y)',
'(y, -y+1/4, 1/8)', '(y+1/2, -y+3/4, 5/8)',
'(-y, -y+3/4, 3/8)', '(-y+1/2, -y+1/4, 7/8)',
'(y+1/2, y+1/4, 7/8)', '(y, y+3/4, 3/8)',
'(-y+1/2, y+3/4, 5/8)', '(-y, y+1/4, 1/8)',
'(7/8, -y, y+3/4)', '(3/8, -y+1/2, y+1/4)',
'(5/8, y, y+1/4)', '(1/8, y+1/2, y+3/4)',
'(1/8, -y+1/2, -y+3/4)', '(5/8, -y, -y+1/4)',
'(3/8, y+1/2, -y+1/4)', '(7/8, y, -y+3/4)',
'(y+3/4, 7/8, -y)', '(y+1/4, 3/8, -y+1/2)',
'(y+1/4, 5/8, y)', '(y+3/4, 1/8, y+1/2)',
'(-y+3/4, 1/8, -y+1/2)', '(-y+1/4, 5/8, -y)',
'(-y+1/4, 3/8, y+1/2)', '(-y+3/4, 7/8, y)',
'(-y, y+3/4, 7/8)', '(-y+1/2, y+1/4, 3/8)',
'(y, y+1/4, 5/8)', '(y+1/2, y+3/4, 1/8)',
'(-y+1/2, -y+3/4, 1/8)', '(-y, -y+1/4, 5/8)',
'(y+1/2, -y+1/4, 3/8)', '(y, -y+3/4, 7/8)'),
'hkl: h=2n+1 or h=4n'),
'96h': (7, ('(x, y, z)', '(x+1/2, y+1/2, z+1/2)',
'(-x+1/2, -y, z+1/2)', '(-x, -y+1/2, z)',
'(-x, y+1/2, -z+1/2)', '(-x+1/2, y, -z)',
'(x+1/2, -y+1/2, -z)', '(x, -y, -z+1/2)',
'(z, x, y)', '(z+1/2, x+1/2, y+1/2)',
'(z+1/2, -x+1/2, -y)', '(z, -x, -y+1/2)',
'(-z+1/2, -x, y+1/2)', '(-z, -x+1/2, y)',
'(-z, x+1/2, -y+1/2)', '(-z+1/2, x, -y)',
'(y, z, x)', '(y+1/2, z+1/2, x+1/2)',
'(-y, z+1/2, -x+1/2)', '(-y+1/2, z, -x)',
'(y+1/2, -z+1/2, -x)', '(y, -z, -x+1/2)',
'(-y+1/2, -z, x+1/2)', '(-y, -z+1/2, x)',
'(y+3/4, x+1/4, -z+1/4)', '(y+1/4, x+3/4, -z+3/4)',
'(-y+3/4, -x+3/4, -z+3/4)',
'(-y+1/4, -x+1/4, -z+1/4)',
'(y+1/4, -x+1/4, z+3/4)', '(y+3/4, -x+3/4, z+1/4)',
'(-y+1/4, x+3/4, z+1/4)', '(-y+3/4, x+1/4, z+3/4)',
'(x+3/4, z+1/4, -y+1/4)', '(x+1/4, z+3/4, -y+3/4)',
'(-x+1/4, z+3/4, y+1/4)', '(-x+3/4, z+1/4, y+3/4)',
'(-x+3/4, -z+3/4, -y+3/4)',
'(-x+1/4, -z+1/4, -y+1/4)',
'(x+1/4, -z+1/4, y+3/4)', '(x+3/4, -z+3/4, y+1/4)',
'(z+3/4, y+1/4, -x+1/4)', '(z+1/4, y+3/4, -x+3/4)',
'(z+1/4, -y+1/4, x+3/4)', '(z+3/4, -y+3/4, x+1/4)',
'(-z+1/4, y+3/4, x+1/4)', '(-z+3/4, y+1/4, x+3/4)',
'(-z+3/4, -y+3/4, -x+3/4)',
'(-z+1/4, -y+1/4, -x+1/4)', '(-x, -y, -z)',
'(-x+1/2, -y+1/2, -z+1/2)', '(x+1/2, y, -z+1/2)',
'(x, y+1/2, -z)', '(x, -y+1/2, z+1/2)',
'(x+1/2, -y, z)', '(-x+1/2, y+1/2, z)',
'(-x, y, z+1/2)', '(-z, -x, -y)',
'(-z+1/2, -x+1/2, -y+1/2)', '(-z+1/2, x+1/2, y)',
'(-z, x, y+1/2)', '(z+1/2, x, -y+1/2)',
'(z, x+1/2, -y)', '(z, -x+1/2, y+1/2)',
'(z+1/2, -x, y)', '(-y, -z, -x)',
'(-y+1/2, -z+1/2, -x+1/2)', '(y, -z+1/2, x+1/2)',
'(y+1/2, -z, x)', '(-y+1/2, z+1/2, x)',
'(-y, z, x+1/2)', '(y+1/2, z, -x+1/2)',
'(y, z+1/2, -x)', '(-y+1/4, -x+3/4, z+3/4)',
'(-y+3/4, -x+1/4, z+1/4)', '(y+1/4, x+1/4, z+1/4)',
'(y+3/4, x+3/4, z+3/4)', '(-y+3/4, x+3/4, -z+1/4)',
'(-y+1/4, x+1/4, -z+3/4)',
'(y+3/4, -x+1/4, -z+3/4)',
'(y+1/4, -x+3/4, -z+1/4)',
'(-x+1/4, -z+3/4, y+3/4)',
'(-x+3/4, -z+1/4, y+1/4)',
'(x+3/4, -z+1/4, -y+3/4)',
'(x+1/4, -z+3/4, -y+1/4)', '(x+1/4, z+1/4, y+1/4)',
'(x+3/4, z+3/4, y+3/4)', '(-x+3/4, z+3/4, -y+1/4)',
'(-x+1/4, z+1/4, -y+3/4)',
'(-z+1/4, -y+3/4, x+3/4)',
'(-z+3/4, -y+1/4, x+1/4)',
'(-z+3/4, y+3/4, -x+1/4)',
'(-z+1/4, y+1/4, -x+3/4)',
'(z+3/4, -y+1/4, -x+3/4)',
'(z+1/4, -y+3/4, -x+1/4)', '(z+1/4, y+1/4, x+1/4)',
'(z+3/4, y+3/4, x+3/4)'),
'hkl: h+k+l=2n, 0kl: k,l=2n, hhl: 2h+l=4n, h00: h=4n')},
}