# 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"),
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6,
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"(0, 0, z)",
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"(0, 0, z)",
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"(3/4, 3/4, z+1/2)",
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"(-x+1/2, 0, z+1/2)",
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"(x, y, z)",
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"(-x+1/2, -y+1/2, z)",
"(x, -y, z)",
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"(x+1/2, -y+1/2, z)",
"(-x, y, z)",
"(-x, y+1/2, z+1/2)",
"(-x+1/2, y, z+1/2)",
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"hk0: h,k=2n, h00: h=2n, 0k0: k=2n, 00l: l=2n",
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"(0, 0, z)",
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"(3/4, 1/4, z+3/4)",
"(1/4, 3/4, z+3/4)",
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),
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4,
(
"(1/4, 0, z)",
"(3/4, 1/2, z)",
"(3/4, 0, -z+1/2)",
"(1/4, 1/2, -z+1/2)",
"(3/4, 0, -z)",
"(1/4, 1/2, -z)",
"(1/4, 0, z+1/2)",
"(3/4, 1/2, z+1/2)",
),
"n/a",
),
"16i": (
7,
(
"(x, y, z)",
"(x+1/2, y+1/2, z)",
"(-x+1/2, -y, z)",
"(-x, -y+1/2, z)",
"(-x, y, -z+1/2)",
"(-x+1/2, y+1/2, -z+1/2)",
"(x+1/2, -y, -z+1/2)",
"(x, -y+1/2, -z+1/2)",
"(-x, -y, -z)",
"(-x+1/2, -y+1/2, -z)",
"(x+1/2, y, -z)",
"(x, y+1/2, -z)",
"(x, -y, z+1/2)",
"(x+1/2, -y+1/2, z+1/2)",
"(-x+1/2, y, z+1/2)",
"(-x, y+1/2, z+1/2)",
),
"n/a",
),
},
"69": {
"4a": (
0,
("(0, 0, 0)", "(0, 1/2, 1/2)", "(1/2, 0, 1/2)", "(1/2, 1/2, 0)"),
None,
),
"4b": (
0,
("(0, 0, 1/2)", "(0, 1/2, 0)", "(1/2, 0, 0)", "(1/2, 1/2, 1/2)"),
None,
),
"8c": (
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)",
),
"hkl: h=2n",
),
"8d": (
0,
(
"(1/4, 0, 1/4)",
"(1/4, 1/2, 3/4)",
"(3/4, 0, 3/4)",
"(3/4, 1/2, 1/4)",
"(3/4, 0, 1/4)",
"(3/4, 1/2, 3/4)",
"(1/4, 0, 3/4)",
"(1/4, 1/2, 1/4)",
),
"hkl: h=2n",
),
"8e": (
0,
(
"(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",
),
"8f": (
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",
),
"8g": (
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)",
),
None,
),
"8h": (
2,
(
"(0, y, 0)",
"(0, y+1/2, 1/2)",
"(1/2, y, 1/2)",
"(1/2, y+1/2, 0)",
"(0, -y, 0)",
"(0, -y+1/2, 1/2)",
"(1/2, -y, 1/2)",
"(1/2, -y+1/2, 0)",
),
None,
),
"8i": (
4,
(
"(0, 0, z)",
"(0, 1/2, z+1/2)",
"(1/2, 0, z+1/2)",
"(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)",
),
None,
),
"16j": (
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)",
"(3/4, 1/4, -z)",
"(3/4, 3/4, -z+1/2)",
"(1/4, 1/4, -z+1/2)",
"(1/4, 3/4, -z)",
"(3/4, 3/4, -z)",
"(3/4, 1/4, -z+1/2)",
"(1/4, 3/4, -z+1/2)",
"(1/4, 1/4, -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",
),
"16k": (
2,
(
"(1/4, y, 1/4)",
"(1/4, y+1/2, 3/4)",
"(3/4, y, 3/4)",
"(3/4, y+1/2, 1/4)",
"(3/4, -y, 1/4)",
"(3/4, -y+1/2, 3/4)",
"(1/4, -y, 3/4)",
"(1/4, -y+1/2, 1/4)",
"(3/4, -y, 3/4)",
"(3/4, -y+1/2, 1/4)",
"(1/4, -y, 1/4)",
"(1/4, -y+1/2, 3/4)",
"(1/4, y, 3/4)",
"(1/4, y+1/2, 1/4)",
"(3/4, y, 1/4)",
"(3/4, y+1/2, 3/4)",
),
"hkl: h=2n",
),
"16l": (
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)",
"(-x, 3/4, 3/4)",
"(-x, 1/4, 1/4)",
"(-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)",
),
"hkl: h=2n",
),
"16m": (
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)",
),
None,
),
"16n": (
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)",
"(-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,
),
"16o": (
3,
(
"(x, y, 0)",
"(x, y+1/2, 1/2)",
"(x+1/2, y, 1/2)",
"(x+1/2, y+1/2, 0)",
"(-x, -y, 0)",
"(-x, -y+1/2, 1/2)",
"(-x+1/2, -y, 1/2)",
"(-x+1/2, -y+1/2, 0)",
"(-x, y, 0)",
"(-x, y+1/2, 1/2)",
"(-x+1/2, y, 1/2)",
"(-x+1/2, y+1/2, 0)",
"(x, -y, 0)",
"(x, -y+1/2, 1/2)",
"(x+1/2, -y, 1/2)",
"(x+1/2, -y+1/2, 0)",
),
None,
),
"32p": (
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, -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",
),
},
"70:1": {
"8a": (
0,
(
"(0, 0, 0)",
"(0, 1/2, 1/2)",
"(1/2, 0, 1/2)",
"(1/2, 1/2, 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)",
),
"hkl: h=2n+1 or h+k+l=4n",
),
"8b": (
0,
(
"(0, 0, 1/2)",
"(0, 1/2, 0)",
"(1/2, 0, 0)",
"(1/2, 1/2, 1/2)",
"(1/4, 1/4, 3/4)",
"(1/4, 3/4, 1/4)",
"(3/4, 1/4, 1/4)",
"(3/4, 3/4, 3/4)",
),
"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, 7/8, 1/8)",
"(7/8, 3/8, 5/8)",
"(3/8, 7/8, 5/8)",
"(3/8, 3/8, 1/8)",
"(7/8, 1/8, 7/8)",
"(7/8, 5/8, 3/8)",
"(3/8, 1/8, 3/8)",
"(3/8, 5/8, 7/8)",
"(1/8, 7/8, 7/8)",
"(1/8, 3/8, 3/8)",
"(5/8, 7/8, 3/8)",
"(5/8, 3/8, 7/8)",
),
"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, 3/8, 5/8)",
"(3/8, 7/8, 1/8)",
"(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",
),
"16e": (
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)",
"(-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)",
),
"hkl: h=2n+1 or h+k+l=4n",
),
"16f": (
2,
(
"(0, y, 0)",
"(0, y+1/2, 1/2)",
"(1/2, y, 1/2)",
"(1/2, y+1/2, 0)",
"(0, -y, 0)",
"(0, -y+1/2, 1/2)",
"(1/2, -y, 1/2)",
"(1/2, -y+1/2, 0)",
"(1/4, -y+1/4, 1/4)",
"(1/4, -y+3/4, 3/4)",
"(3/4, -y+1/4, 3/4)",
"(3/4, -y+3/4, 1/4)",
"(1/4, y+1/4, 1/4)",
"(1/4, y+3/4, 3/4)",
"(3/4, y+1/4, 3/4)",
"(3/4, y+3/4, 1/4)",
),
"hkl: h=2n+1 or h+k+l=4n",
),
"16g": (
4,
(
"(0, 0, z)",
"(0, 1/2, z+1/2)",
"(1/2, 0, z+1/2)",
"(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)",
"(y, -x, z+3/4)",
),
"00l: l=4n",
)
},
"77": {
"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": (
7,
("(x, y, z)", "(-x, -y, z)", "(-y, x, z+1/2)", "(y, -x, z+1/2)"),
"00l: l=2n",
),
},
"78": {
"4a": (
7,
(
"(x, y, z)",
"(-x, -y, z+1/2)",
"(-y, x, z+3/4)",
"(y, -x, z+1/4)",
),
"00l: l=4n",
)
},
"79": {
"2a": (4, ("(0, 0, z)", "(1/2, 1/2, z+1/2)"), None),
"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)",
"(-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",
),
},
"80": {
"4a": (
4,
(
"(0, 0, z)",
"(1/2, 1/2, z+1/2)",
"(0, 1/2, z+1/4)",
"(1/2, 0, z+3/4)",
),
"hkl: l=2n+1 or 2h+l=4n",
),
"8b": (
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)",
),
"hkl: h+k+l=2n, hk0: h+k=2n, 0kl: k+l=2n, hhl: l=2n, "
"00l: l=4n, h00: h=2n",
),
},
"81": {
"1a": (0, ("(0, 0, 0)",), None),
"1b": (0, ("(0, 0, 1/2)",), None),
"1c": (0, ("(1/2, 1/2, 0)",), None),
"1d": (0, ("(1/2, 1/2, 1/2)",), None),
"2e": (4, ("(0, 0, z)", "(0, 0, -z)"), None),
"2f": (4, ("(1/2, 1/2, z)", "(1/2, 1/2, -z)"), None),
"2g": (4, ("(0, 1/2, z)", "(1/2, 0, -z)"), "hk0: h+k=2n"),
"4h": (
7,
("(x, y, z)", "(-x, -y, z)", "(y, -x, -z)", "(-y, x, -z)"),
None,
),
},
"82": {
"2a": (0, ("(0, 0, 0)", "(1/2, 1/2, 1/2)"), None),
"2b": (0, ("(0, 0, 1/2)", "(1/2, 1/2, 0)"), None),
"2c": (0, ("(0, 1/2, 1/4)", "(1/2, 0, 3/4)"), None),
"2d": (0, ("(0, 1/2, 3/4)", "(1/2, 0, 1/4)"), None),
"4e": (
4,
(
"(0, 0, z)",
"(1/2, 1/2, z+1/2)",
"(0, 0, -z)",
"(1/2, 1/2, -z+1/2)",
),
None,
),
"4f": (
4,
(
"(0, 1/2, z)",
"(1/2, 0, z+1/2)",
"(1/2, 0, -z)",
"(0, 1/2, -z+1/2)",
),
None,
),
"8g": (
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)",
),
"hkl: h+k+l=2n, hk0: h+k=2n, 0kl: k+l=2n, hhl: l=2n, "
"00l: l=2n, h00: h=2n",
),
},
"83": {
"1a": (0, ("(0, 0, 0)",), None),
"1b": (0, ("(0, 0, 1/2)",), None),
"1c": (0, ("(1/2, 1/2, 0)",), None),
"1d": (0, ("(1/2, 1/2, 1/2)",), None),
"2e": (0, ("(0, 1/2, 0)", "(1/2, 0, 0)"), "hkl: h+k=2n"),
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"(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)", "(1/2, 0, 3/4)"),
"hkl: l=2n+1 or 2h+l=4n",
),
"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)",
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"(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",
),
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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)",
"(3/4, x+1/2, 3/8)",
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"(1/4, -x+1/2, 3/8)",
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"(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)",
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"(-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)",
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"(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)",
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"(-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)",
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"(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)",
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"(-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)",
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"(-x+1/2, x+1/4, 5/8)",
"(x+1/2, -x+1/4, 5/8)",
"(x, -x+3/4, 1/8)",
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"(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)",
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"(y+1/4, 1/4, z+3/4)",
"(y+3/4, 3/4, z+1/4)",
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"(0, y+1/2, -z)",
"(0, -y, -z)",
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"(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)",
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"(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)",
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"(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)",
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"(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)",
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"(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)",
"(0, 1/2, -z+1/4)",
"(1/2, 0, -z+3/4)",
"(0, 0, -z)",
"(1/2, 1/2, -z+1/2)",
"(1/2, 1/2, z)",
"(0, 0, z+1/2)",
"(1/2, 0, z+1/4)",
"(0, 1/2, z+3/4)",
),
"hkl: 2h+l=4n",
),
"16e": (
2,
(
"(1/4, y, 1/8)",
"(3/4, y+1/2, 5/8)",
"(1/4, -y+1/2, 5/8)",
"(3/4, -y, 1/8)",
"(-y, 3/4, 3/8)",
"(-y+1/2, 1/4, 7/8)",
"(y+1/2, 3/4, 7/8)",
"(y, 1/4, 3/8)",
"(3/4, -y+1/2, 1/8)",
"(1/4, -y, 5/8)",
"(3/4, y, 5/8)",
"(1/4, y+1/2, 1/8)",
"(y, 3/4, 7/8)",
"(y+1/2, 1/4, 3/8)",
"(-y+1/2, 3/4, 3/8)",
"(-y, 1/4, 7/8)",
),
"hkl: l=2n+1 or h=2n",
),
"16f": (
1,
(
"(x, x, 1/4)",
"(x+1/2, x+1/2, 3/4)",
"(-x+1/2, -x+1/2, 3/4)",
"(-x, -x, 1/4)",
"(-x, x+1/2, 1/2)",
"(-x+1/2, x, 0)",
"(x+1/2, -x, 0)",
"(x, -x+1/2, 1/2)",
"(-x, -x+1/2, 0)",
"(-x+1/2, -x, 1/2)",
"(x+1/2, x, 1/2)",
"(x, x+1/2, 0)",
"(x, -x, 3/4)",
"(x+1/2, -x+1/2, 1/4)",
"(-x+1/2, x+1/2, 1/4)",
"(-x, x, 3/4)",
),
"hkl: l=2n+1 or 2h+l=4n",
),
"32g": (
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+1/4)",
"(-x, y+1/2, -z+3/4)",
"(x, -y+1/2, -z+3/4)",
"(x+1/2, -y, -z+1/4)",
"(y+1/2, x+1/2, -z)",
"(y, x, -z+1/2)",
"(-y, -x, -z+1/2)",
"(-y+1/2, -x+1/2, -z)",
"(-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)",
"(x, -y, z+1/2)",
"(-x, y, z+1/2)",
"(-x+1/2, y+1/2, z)",
"(-y+1/2, -x, z+1/4)",
"(-y, -x+1/2, z+3/4)",
"(y, x+1/2, z+3/4)",
"(y+1/2, x, z+1/4)",
),
"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",
),
},
"142:2": {
"8a": (
0,
(
"(0, 1/4, 3/8)",
"(1/2, 3/4, 7/8)",
"(0, 3/4, 5/8)",
"(1/2, 1/4, 1/8)",
"(1/2, 1/4, 5/8)",
"(0, 3/4, 1/8)",
"(1/2, 3/4, 3/8)",
"(0, 1/4, 7/8)",
),
"n/a",
),
"8b": (
0,
(
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"(1/2, 3/4, 5/8)",
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),
"n/a",
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"16c": (
0,
(
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"(3/4, 1/4, 1/4)",
"(1/4, 1/4, 1/4)",
"(3/4, 3/4, 3/4)",
),
"n/a",
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"16d": (
4,
(
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"(1/2, 1/4, z+3/4)",
"(1/2, 1/4, -z)",
"(0, 3/4, -z+1/2)",
"(1/2, 3/4, -z+3/4)",
"(0, 1/4, -z+1/4)",
"(0, 3/4, -z)",
"(1/2, 1/4, -z+1/2)",
"(0, 1/4, -z+3/4)",
"(1/2, 3/4, -z+1/4)",
"(1/2, 3/4, z)",
"(0, 1/4, z+1/2)",
"(1/2, 1/4, z+1/4)",
"(0, 3/4, z+3/4)",
),
"n/a",
),
"16e": (
1,
(
"(x, 0, 1/4)",
"(x+1/2, 1/2, 3/4)",
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"(-x, 1/2, 1/4)",
"(1/4, x+3/4, 1/2)",
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"(3/4, -x+3/4, 1/2)",
"(-x, 0, 3/4)",
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"(x+1/2, 0, 1/4)",
"(x, 1/2, 3/4)",
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"(1/4, -x+3/4, 0)",
"(3/4, x+3/4, 0)",
"(1/4, x+1/4, 1/2)",
),
"n/a",
),
"16f": (
1,
(
"(x, x+1/4, 1/8)",
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"(-x+1/2, -x+3/4, 5/8)",
"(-x, -x+1/4, 1/8)",
"(-x, x+3/4, 3/8)",
"(-x+1/2, x+1/4, 7/8)",
"(x+1/2, -x+1/4, 7/8)",
"(x, -x+3/4, 3/8)",
"(-x, -x+3/4, 7/8)",
"(-x+1/2, -x+1/4, 3/8)",
"(x+1/2, x+1/4, 3/8)",
"(x, x+3/4, 7/8)",
"(x, -x+1/4, 5/8)",
"(x+1/2, -x+3/4, 1/8)",
"(-x+1/2, x+3/4, 1/8)",
"(-x, x+1/4, 5/8)",
),
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"(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, -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)",
),
"hkl: h+k,h+l,k+l=2n, 0kl: k,l=2n, hhl: h+l=2n, h00: h=2n",
),
},
"203:1": {
"8a": (
0,
(
"(0, 0, 0)",
"(0, 1/2, 1/2)",
"(1/2, 0, 1/2)",
"(1/2, 1/2, 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)",
),
"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)",
"(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+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, 7/8, 1/8)",
"(7/8, 3/8, 5/8)",
"(3/8, 7/8, 5/8)",
"(3/8, 3/8, 1/8)",
"(7/8, 1/8, 7/8)",
"(7/8, 5/8, 3/8)",
"(3/8, 1/8, 3/8)",
"(3/8, 5/8, 7/8)",
"(1/8, 7/8, 7/8)",
"(1/8, 3/8, 3/8)",
"(5/8, 7/8, 3/8)",
"(5/8, 3/8, 7/8)",
),
"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, 3/8, 5/8)",
"(3/8, 7/8, 1/8)",
"(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)",
"(1/8, 5/8, 1/8)",
"(1/8, 1/8, 5/8)",
"(3/8, 3/8, 3/8)",
"(3/8, 7/8, 7/8)",
"(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)",
"(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",
),
"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)",
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),
"hkl: h+k+l=2n or h=2n+1, k=4n, l=4n+2",
),
"8g": (
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)",
),
"0kl: k+l=2n",
),
"12h": (
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",
),
"12i": (
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, hhl: l=2n",
),
"12j": (
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, hhl: l=2n",
),
"12k": (
2,
(
"(1/4, y, -y+1/2)",
"(3/4, -y, -y+1/2)",
"(3/4, y, y+1/2)",
"(1/4, -y, y+1/2)",
"(-y+1/2, 1/4, y)",
"(-y+1/2, 3/4, -y)",
"(y+1/2, 3/4, y)",
"(y+1/2, 1/4, -y)",
"(y, -y+1/2, 1/4)",
"(-y, -y+1/2, 3/4)",
"(y, y+1/2, 3/4)",
"(-y, y+1/2, 1/4)",
),
None,
),
"12l": (
2,
(
"(1/4, y, y+1/2)",
"(3/4, -y, y+1/2)",
"(3/4, y, -y+1/2)",
"(1/4, -y, -y+1/2)",
"(y+1/2, 1/4, y)",
"(y+1/2, 3/4, -y)",
"(-y+1/2, 3/4, y)",
"(-y+1/2, 1/4, -y)",
"(y, y+1/2, 1/4)",
"(-y, y+1/2, 3/4)",
"(y, -y+1/2, 3/4)",
"(-y, -y+1/2, 1/4)",
),
None,
),
"24m": (
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)",
),
"h00: h=2n",
),
},
"209": {
"4a": (
0,
("(0, 0, 0)", "(0, 1/2, 1/2)", "(1/2, 0, 1/2)", "(1/2, 1/2, 0)"),
None,
),
"4b": (
0,
("(1/2, 1/2, 1/2)", "(1/2, 0, 0)", "(0, 1/2, 0)", "(0, 0, 1/2)"),
None,
),
"8c": (
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)",
"(1/4, 1/4, 3/4)",
"(1/4, 3/4, 1/4)",
"(3/4, 1/4, 1/4)",
"(3/4, 3/4, 3/4)",
),
"hkl: h=2n",
),
"24d": (
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",
),
"24e": (
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)",
),
None,
),
"32f": (
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, 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)",
),
None,
),
"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",
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"4b": (
0,
(
"(7/8, 7/8, 7/8)",
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),
"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",
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1,
(
"(x, x, x)",
"(-x+1/2, -x, x+1/2)",
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"(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)",
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"0kl: k=2n+1 or l=2n+1 or k+l=4n",
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2,
(
"(1/8, y, y+1/4)",
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"(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",
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"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)",
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"(3/4, 3/8, 0)",
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"(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)",
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"(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)",
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"(-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",
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1,
(
"(x, 0, 1/4)",
"(x+1/2, 1/2, 3/4)",
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"(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)",
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"(x+3/4, 1/2, 1/4)",
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"(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",
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2,
(
"(1/8, y, y+1/4)",
"(5/8, y+1/2, y+3/4)",
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"(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)",
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"(-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)",
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"(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)",
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"(1/8, -y, y+1/4)",
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"(y+1/4, 7/8, y+1/2)",
"(y+3/4, 3/8, y)",
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"(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,
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7,
(
"(x, y, z)",
"(x+1/2, y+1/2, z+1/2)",
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"(x+1/2, -y+1/2, -z)",
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"(z, x, y)",
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"(z+1/2, -x+1/2, -y)",
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"(y, -z, -x+1/2)",
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"(-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",
),
},
"215": {
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"3c": (0, ("(0, 1/2, 1/2)", "(1/2, 0, 1/2)", "(1/2, 1/2, 0)"), None),
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1,
("(x, x, x)", "(-x, -x, x)", "(-x, x, -x)", "(x, -x, -x)"),
None,
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1,
(
"(x, 0, 0)",
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None,
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1,
(
"(x, 1/2, 1/2)",
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None,
),
"12h": (
1,
(
"(x, 1/2, 0)",
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"(0, 1/2, -x)",
),
None,
),
"12i": (
5,
(
"(x, x, z)",
"(-x, -x, z)",
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"(z, x, x)",
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"(-z, -x, x)",
"(-z, x, -x)",
"(x, z, x)",
"(-x, z, -x)",
"(x, -z, -x)",
"(-x, -z, x)",
),
None,
),
"24j": (
7,
(
"(x, y, z)",
"(-x, -y, z)",
"(-x, y, -z)",
"(x, -y, -z)",
"(z, x, y)",
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"(x, z, y)",
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"(x, -z, -y)",
"(z, y, x)",
"(z, -y, -x)",
"(-z, y, -x)",
"(-z, -y, x)",
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None,
),
},
"216": {
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0,
("(0, 0, 0)", "(0, 1/2, 1/2)", "(1/2, 0, 1/2)", "(1/2, 1/2, 0)"),
None,
),
"4b": (
0,
("(1/2, 1/2, 1/2)", "(1/2, 0, 0)", "(0, 1/2, 0)", "(0, 0, 1/2)"),
None,
),
"4c": (
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)",
),
None,
),
"4d": (
0,
(
"(3/4, 3/4, 3/4)",
"(3/4, 1/4, 1/4)",
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"(1/4, 1/4, 3/4)",
),
None,
),
"16e": (
1,
(
"(x, x, x)",
"(x, x+1/2, x+1/2)",
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"(-x+1/2, -x, x+1/2)",
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"(-x+1/2, x, -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)",
),
None,
),
"24f": (
1,
(
"(x, 0, 0)",
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"(-x+1/2, 1/2, 0)",
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"(1/2, -x, 1/2)",
"(1/2, -x+1/2, 0)",
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"(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)",
),
None,
),
"24g": (
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)",
),
None,
),
"48h": (
5,
(
"(x, x, z)",
"(x, x+1/2, z+1/2)",
"(x+1/2, x, z+1/2)",
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"(-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)",
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"(-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)",
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7,
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"hkl: h+k,h+l,k+l=2n, 0kl: k,l=2n, hhl: h+l=2n, h00: h=2n",
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1,
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None,
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1,
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None,
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5,
(
"(x, x, z)",
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7,
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"(z, -y, -x)",
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0,
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0,
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0,
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1,
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1,
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"hkl: h=2n",
),
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1,
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"(1/4, 3/4, x+1/2)",
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"(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)",
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"(y, x, z+1/2)",
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"(y+1/2, -x+1/2, -z+1/2)",
"(y+1/2, -x, -z)",
"(y, -x+1/2, -z)",
"(y, -x, -z+1/2)",
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"(x+1/2, -z+1/2, -y+1/2)",
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"(z+1/2, y+1/2, x+1/2)",
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"(z, y+1/2, x)",
"(z, y, x+1/2)",
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"(z+1/2, -y, -x)",
"(z, -y+1/2, -x)",
"(z, -y, -x+1/2)",
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"(-z+1/2, y, -x)",
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"(-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",
),
},
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0,
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"k=8n+3, l=4n or h=8n+1, k=8n+5, l=4n or h=8n+7, "
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0,
(
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"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, "
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1,
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"(x, x, x)",
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1,
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"(x, 0, 1/4)",
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7,
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"(y+3/4, -x+1/4, -z+3/4)",
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"(-x+3/4, z+3/4, -y+1/4)",
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"(-x+1/4, -z+3/4, y+3/4)",
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"(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)",
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"(-z+1/4, -y+3/4, x+3/4)",
"(-z+3/4, -y+1/4, x+1/4)",
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"3c": (0, ("(0, 1/2, 1/2)", "(1/2, 0, 1/2)", "(1/2, 1/2, 0)"), None),
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1,
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None,
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1,
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None,
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1,
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2,
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2,
(
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None,
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6,
(
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6,
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None,
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5,
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None,
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7,
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None,
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},
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0,
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0,
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1,
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),
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1,
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"(1/2, x+1/2, 0)",
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"(x+1/2, 0, 1/2)",
"(0, 1/2, x+1/2)",
"(0, 1/2, -x+1/2)",
),
"hkl: h+k+l=2n",
),
"24h": (
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)",
"(1/2, -y+1/2, -y+1/2)",
"(1/2, y+1/2, -y+1/2)",
"(1/2, -y+1/2, y+1/2)",
"(1/2, y+1/2, y+1/2)",
"(-y+1/2, 1/2, -y+1/2)",
"(-y+1/2, 1/2, y+1/2)",
"(y+1/2, 1/2, -y+1/2)",
"(y+1/2, 1/2, y+1/2)",
"(-y+1/2, -y+1/2, 1/2)",
"(y+1/2, -y+1/2, 1/2)",
"(-y+1/2, y+1/2, 1/2)",
"(y+1/2, y+1/2, 1/2)",
),
"hkl: h+k+l=2n",
),
"48i": (
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, 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)",
"(-x+1/2, -y+1/2, -z+1/2)",
"(x+1/2, y+1/2, -z+1/2)",
"(x+1/2, -y+1/2, z+1/2)",
"(-x+1/2, y+1/2, z+1/2)",
"(-z+1/2, -x+1/2, -y+1/2)",
"(-z+1/2, x+1/2, y+1/2)",
"(z+1/2, x+1/2, -y+1/2)",
"(z+1/2, -x+1/2, y+1/2)",
"(-y+1/2, -z+1/2, -x+1/2)",
"(y+1/2, -z+1/2, x+1/2)",
"(-y+1/2, z+1/2, x+1/2)",
"(y+1/2, z+1/2, -x+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, -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)",
),
"0kl: k+l=2n, hhl: l=2n, h00: h=2n",
),
},
"222:2": {
"2a": (0, ("(1/4, 1/4, 1/4)", "(3/4, 3/4, 3/4)"), "n/a"),
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0,
(
"(3/4, 1/4, 1/4)",
"(1/4, 3/4, 1/4)",
"(1/4, 1/4, 3/4)",
"(1/4, 3/4, 3/4)",
"(3/4, 1/4, 3/4)",
"(3/4, 3/4, 1/4)",
),
"n/a",
),
"8c": (
0,
(
"(0, 0, 0)",
"(1/2, 1/2, 0)",
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"(0, 1/2, 1/2)",
"(0, 0, 1/2)",
"(1/2, 1/2, 1/2)",
"(0, 1/2, 0)",
"(1/2, 0, 0)",
),
"n/a",
),
"12d": (
0,
(
"(0, 3/4, 1/4)",
"(1/2, 3/4, 1/4)",
"(1/4, 0, 3/4)",
"(1/4, 1/2, 3/4)",
"(3/4, 1/4, 0)",
"(3/4, 1/4, 1/2)",
"(3/4, 0, 1/4)",
"(3/4, 1/2, 1/4)",
"(0, 1/4, 3/4)",
"(1/2, 1/4, 3/4)",
"(1/4, 3/4, 1/2)",
"(1/4, 3/4, 0)",
),
"n/a",
),
"12e": (
1,
(
"(x, 1/4, 1/4)",
"(-x+1/2, 1/4, 1/4)",
"(1/4, x, 1/4)",
"(1/4, -x+1/2, 1/4)",
"(1/4, 1/4, x)",
"(1/4, 1/4, -x+1/2)",
"(-x, 3/4, 3/4)",
"(x+1/2, 3/4, 3/4)",
"(3/4, -x, 3/4)",
"(3/4, x+1/2, 3/4)",
"(3/4, 3/4, -x)",
"(3/4, 3/4, x+1/2)",
),
"n/a",
),
"16f": (
1,
(
"(x, x, x)",
"(-x+1/2, -x+1/2, x)",
"(-x+1/2, x, -x+1/2)",
"(x, -x+1/2, -x+1/2)",
"(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, -x, -x)",
"(x+1/2, x+1/2, -x)",
"(x+1/2, -x, x+1/2)",
"(-x, x+1/2, x+1/2)",
"(-x, -x, x+1/2)",
"(x+1/2, x+1/2, x+1/2)",
"(-x, x+1/2, -x)",
"(x+1/2, -x, -x)",
),
"n/a",
),
"24g": (
1,
(
"(x, 3/4, 1/4)",
"(-x+1/2, 3/4, 1/4)",
"(1/4, x, 3/4)",
"(1/4, -x+1/2, 3/4)",
"(3/4, 1/4, x)",
"(3/4, 1/4, -x+1/2)",
"(3/4, x, 1/4)",
"(3/4, -x+1/2, 1/4)",
"(x, 1/4, 3/4)",
"(-x+1/2, 1/4, 3/4)",
"(1/4, 3/4, -x+1/2)",
"(1/4, 3/4, x)",
"(-x, 1/4, 3/4)",
"(x+1/2, 1/4, 3/4)",
"(3/4, -x, 1/4)",
"(3/4, x+1/2, 1/4)",
"(1/4, 3/4, -x)",
"(1/4, 3/4, x+1/2)",
"(1/4, -x, 3/4)",
"(1/4, x+1/2, 3/4)",
"(-x, 3/4, 1/4)",
"(x+1/2, 3/4, 1/4)",
"(3/4, 1/4, x+1/2)",
"(3/4, 1/4, -x)",
),
"n/a",
),
"24h": (
2,
(
"(1/4, y, y)",
"(1/4, -y+1/2, y)",
"(1/4, y, -y+1/2)",
"(1/4, -y+1/2, -y+1/2)",
"(y, 1/4, y)",
"(y, 1/4, -y+1/2)",
"(-y+1/2, 1/4, y)",
"(-y+1/2, 1/4, -y+1/2)",
"(y, y, 1/4)",
"(-y+1/2, y, 1/4)",
"(y, -y+1/2, 1/4)",
"(-y+1/2, -y+1/2, 1/4)",
"(3/4, -y, -y)",
"(3/4, y+1/2, -y)",
"(3/4, -y, y+1/2)",
"(3/4, y+1/2, y+1/2)",
"(-y, 3/4, -y)",
"(-y, 3/4, y+1/2)",
"(y+1/2, 3/4, -y)",
"(y+1/2, 3/4, y+1/2)",
"(-y, -y, 3/4)",
"(y+1/2, -y, 3/4)",
"(-y, y+1/2, 3/4)",
"(y+1/2, y+1/2, 3/4)",
),
"n/a",
),
"48i": (
7,
(
"(x, y, z)",
"(-x+1/2, -y+1/2, z)",
"(-x+1/2, y, -z+1/2)",
"(x, -y+1/2, -z+1/2)",
"(z, x, y)",
"(z, -x+1/2, -y+1/2)",
"(-z+1/2, -x+1/2, y)",
"(-z+1/2, x, -y+1/2)",
"(y, z, x)",
"(-y+1/2, z, -x+1/2)",
"(y, -z+1/2, -x+1/2)",
"(-y+1/2, -z+1/2, x)",
"(y, x, -z+1/2)",
"(-y+1/2, -x+1/2, -z+1/2)",
"(y, -x+1/2, z)",
"(-y+1/2, x, z)",
"(x, z, -y+1/2)",
"(-x+1/2, z, y)",
"(-x+1/2, -z+1/2, -y+1/2)",
"(x, -z+1/2, y)",
"(z, y, -x+1/2)",
"(z, -y+1/2, x)",
"(-z+1/2, y, x)",
"(-z+1/2, -y+1/2, -x+1/2)",
"(-x, -y, -z)",
"(x+1/2, y+1/2, -z)",
"(x+1/2, -y, z+1/2)",
"(-x, y+1/2, z+1/2)",
"(-z, -x, -y)",
"(-z, x+1/2, y+1/2)",
"(z+1/2, x+1/2, -y)",
"(z+1/2, -x, y+1/2)",
"(-y, -z, -x)",
"(y+1/2, -z, x+1/2)",
"(-y, z+1/2, x+1/2)",
"(y+1/2, z+1/2, -x)",
"(-y, -x, z+1/2)",
"(y+1/2, x+1/2, z+1/2)",
"(-y, x+1/2, -z)",
"(y+1/2, -x, -z)",
"(-x, -z, y+1/2)",
"(x+1/2, -z, -y)",
"(x+1/2, z+1/2, y+1/2)",
"(-x, z+1/2, -y)",
"(-z, -y, x+1/2)",
"(-z, y+1/2, -x)",
"(z+1/2, -y, -x)",
"(z+1/2, y+1/2, x+1/2)",
),
"n/a",
),
},
"223": {
"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, 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",
),
"6d": (
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",
),
"8e": (
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)",
"(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,l=2n",
),
"12f": (
1,
(
"(x, 0, 0)",
"(-x, 0, 0)",
"(0, x, 0)",
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"(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, 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",
),
"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)",
"(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",
),
"16i": (
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)",
"(-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",
),
"24j": (
2,
(
"(1/4, y, y+1/2)",
"(3/4, -y, y+1/2)",
"(3/4, y, -y+1/2)",
"(1/4, -y, -y+1/2)",
"(y+1/2, 1/4, y)",
"(y+1/2, 3/4, -y)",
"(-y+1/2, 3/4, y)",
"(-y+1/2, 1/4, -y)",
"(y, y+1/2, 1/4)",
"(-y, y+1/2, 3/4)",
"(y, -y+1/2, 3/4)",
"(-y, -y+1/2, 1/4)",
"(3/4, -y, -y+1/2)",
"(1/4, y, -y+1/2)",
"(1/4, -y, y+1/2)",
"(3/4, y, y+1/2)",
"(-y+1/2, 3/4, -y)",
"(-y+1/2, 1/4, y)",
"(y+1/2, 1/4, -y)",
"(y+1/2, 3/4, y)",
"(-y, -y+1/2, 3/4)",
"(y, -y+1/2, 1/4)",
"(-y, y+1/2, 1/4)",
"(y, y+1/2, 3/4)",
),
"hkl: h=2n",
),
"24k": (
6,
(
"(0, y, z)",
"(0, -y, z)",
"(0, y, -z)",
"(0, -y, -z)",
"(z, 0, y)",
"(z, 0, -y)",
"(-z, 0, y)",
"(-z, 0, -y)",
"(y, z, 0)",
"(-y, z, 0)",
"(y, -z, 0)",
"(-y, -z, 0)",
"(y+1/2, 1/2, -z+1/2)",
"(-y+1/2, 1/2, -z+1/2)",
"(y+1/2, 1/2, z+1/2)",
"(-y+1/2, 1/2, z+1/2)",
"(1/2, z+1/2, -y+1/2)",
"(1/2, z+1/2, y+1/2)",
"(1/2, -z+1/2, -y+1/2)",
"(1/2, -z+1/2, y+1/2)",
"(z+1/2, y+1/2, 1/2)",
"(z+1/2, -y+1/2, 1/2)",
"(-z+1/2, y+1/2, 1/2)",
"(-z+1/2, -y+1/2, 1/2)",
),
None,
),
"48l": (
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)",
"(-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",
),
},
"224:1": {
"2a": (0, ("(0, 0, 0)", "(1/2, 1/2, 1/2)"), "hkl: h+k+l=2n"),
"4b": (
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",
),
"4c": (
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",
),
"6d": (
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",
),
"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)",
),
None,
),
"12f": (
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)",
"(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",
),
"12g": (
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",
),
"24h": (
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)",
"(-x+1/2, 1/2, 0)",
"(x+1/2, 1/2, 0)",
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None,
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2,
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None,
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5,
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"(x, x, z)",
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None,
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7,
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0,
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1,
(
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2,
(
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2,
(
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5,
(
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7,
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"(z, -y+1/2, -x+1/2)",
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"n/a",
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},
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"4a": (
0,
("(0, 0, 0)", "(0, 1/2, 1/2)", "(1/2, 0, 1/2)", "(1/2, 1/2, 0)"),
None,
),
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0,
("(1/2, 1/2, 1/2)", "(1/2, 0, 0)", "(0, 1/2, 0)", "(0, 0, 1/2)"),
None,
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0,
(
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"hkl: h=2n",
),
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0,
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"(1/4, 3/4, 0)",
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),
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1,
(
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"(1/2, 1/2, -x)",
),
None,
),
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1,
(
"(x, x, x)",
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None,
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1,
(
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"hkl: h=2n",
),
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2,
(
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"(-y, -y+1/2, 1/2)",
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None,
),
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2,
(
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"(-y, -y+1/2, 0)",
"(-y+1/2, -y, 0)",
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),
None,
),
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6,
(
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"(-z, -y+1/2, 1/2)",
"(-z+1/2, -y, 1/2)",
"(-z+1/2, -y+1/2, 0)",
),
None,
),
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5,
(
"(x, x, z)",
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"(-z, -x+1/2, -x+1/2)",
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),
None,
),
"192l": (
7,
(
"(x, y, z)",
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"(x+1/2, -z+1/2, -y)",
"(x, z, y)",
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"(x+1/2, z, y+1/2)",
"(x+1/2, z+1/2, y)",
"(-x, z, -y)",
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"(-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)",
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"(-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",
),
},
"226": {
"8a": (
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",
),
"8b": (
0,
(
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"(1/2, 1/2, 1/2)",
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"(0, 1/2, 0)",
"(0, 0, 1/2)",
),
"hkl: h=2n",
),
"24c": (
0,
(
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"(0, 0, 3/4)",
"(0, 1/2, 1/4)",
"(1/2, 0, 1/4)",
"(1/2, 1/2, 3/4)",
),
"hkl: h=2n",
),
"24d": (
0,
(
"(0, 1/4, 1/4)",
"(0, 3/4, 3/4)",
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"(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",
),
"48e": (
1,
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"(x, 0, 0)",
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"(0, 0, x+1/2)",
),
"hkl: h=2n",
),
"48f": (
1,
(
"(x, 1/4, 1/4)",
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"(3/4, 3/4, x)",
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"(3/4, -x, 3/4)",
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"(1/4, -x, 1/4)",
"(1/4, -x+1/2, 3/4)",
"(3/4, x, 1/4)",
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"(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",
),
"64g": (
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)",
"(-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)",
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"(-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",
),
"96h": (
2,
(
"(1/4, y, y)",
"(1/4, y+1/2, y+1/2)",
"(3/4, y, y+1/2)",
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"(y, 1/4, y)",
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"(-y, y, 3/4)",
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"(y, -y, 3/4)",
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"(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)",
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"(-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",
),
"96i": (
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)",
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"(1/2, y, -z+1/2)",
"(1/2, y+1/2, -z)",
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"(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)",
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"(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)",
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"(-x, y, -z)",
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"(z, x, y)",
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"(z+1/2, x, y+1/2)",
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"(z+1/2, -x, -y+1/2)",
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"(y, -z, -x)",
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"(y+1/2, -z, -x+1/2)",
"(y+1/2, -z+1/2, -x)",
"(-y, -z, x)",
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"(-y+1/2, -x, -z)",
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"(-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)",
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"(-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)",
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"(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)",
"(-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)",
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"hkl: h+k=2n, h+l,k+l=2n, 0kl: k+l=4n, k,l=2n, "
"hhl: h+l=2n, h00: h=4n",
),
},
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"(-y+3/4, 1/4, -y+1/2)",
"(-y+3/4, 1/2, y+1/4)",
"(-y+3/4, 0, y+3/4)",
"(-y+1/4, 1/2, y+3/4)",
"(-y+1/4, 0, y+1/4)",
"(-y, y, 0)",
"(-y, y+1/2, 1/2)",
"(-y+1/2, y, 1/2)",
"(-y+1/2, y+1/2, 0)",
"(y+3/4, y+1/2, 1/4)",
"(y+3/4, y, 3/4)",
"(y+1/4, y+1/2, 3/4)",
"(y+1/4, y, 1/4)",
"(-y+1/2, -y+1/4, 3/4)",
"(-y+1/2, -y+3/4, 1/4)",
"(-y, -y+1/4, 1/4)",
"(-y, -y+3/4, 3/4)",
"(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",
),
"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+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+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)",
"(-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+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)",
"(-y+1/2, x+1/4, z+3/4)",
"(-y, x+3/4, z+3/4)",
"(-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)",
"(-z+1/2, y+1/4, x+3/4)",
"(-z, y+3/4, x+3/4)",
"(-z, y+1/4, x+1/4)",
"(-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+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+1/4, -x+3/4, z+1/2)",
"(-y+1/4, -x+1/4, z)",
"(-y+3/4, -x+3/4, z)",
"(-y+3/4, -x+1/4, z+1/2)",
"(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+3/4, x+1/2, -z+1/4)",
"(-y+3/4, x, -z+3/4)",
"(-y+1/4, x+1/2, -z+3/4)",
"(-y+1/4, x, -z+1/4)",
"(y+1/2, -x+1/4, -z+3/4)",
"(y+1/2, -x+3/4, -z+1/4)",
"(y, -x+1/4, -z+1/4)",
"(y, -x+3/4, -z+3/4)",
"(-x+1/4, -z+3/4, y+1/2)",
"(-x+1/4, -z+1/4, y)",
"(-x+3/4, -z+3/4, y)",
"(-x+3/4, -z+1/4, y+1/2)",
"(x+1/2, -z+1/4, -y+3/4)",
"(x+1/2, -z+3/4, -y+1/4)",
"(x, -z+1/4, -y+1/4)",
"(x, -z+3/4, -y+3/4)",
"(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+3/4, z+1/2, -y+1/4)",
"(-x+3/4, z, -y+3/4)",
"(-x+1/4, z+1/2, -y+3/4)",
"(-x+1/4, z, -y+1/4)",
"(-z+1/4, -y+3/4, x+1/2)",
"(-z+1/4, -y+1/4, x)",
"(-z+3/4, -y+3/4, x)",
"(-z+3/4, -y+1/4, x+1/2)",
"(-z+3/4, y+1/2, -x+1/4)",
"(-z+3/4, y, -x+3/4)",
"(-z+1/4, y+1/2, -x+3/4)",
"(-z+1/4, y, -x+1/4)",
"(z+1/2, -y+1/4, -x+3/4)",
"(z+1/2, -y+3/4, -x+1/4)",
"(z, -y+1/4, -x+1/4)",
"(z, -y+3/4, -x+3/4)",
"(z, y, x)",
"(z, y+1/2, x+1/2)",
"(z+1/2, y, x+1/2)",
"(z+1/2, y+1/2, x)",
),
"n/a",
),
},
"228:1": {
"16a": (
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)",
"(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, 0)",
"(0, 0, 1/2)",
"(1/2, 1/2, 1/2)",
"(1/2, 0, 0)",
),
"hkl: h+k+l=4n",
),
"32b": (
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)",
"(5/8, 5/8, 5/8)",
"(5/8, 1/8, 1/8)",
"(1/8, 5/8, 1/8)",
"(1/8, 1/8, 5/8)",
"(7/8, 3/8, 1/8)",
"(7/8, 7/8, 5/8)",
"(3/8, 3/8, 5/8)",
"(3/8, 7/8, 1/8)",
"(3/8, 1/8, 7/8)",
"(3/8, 5/8, 3/8)",
"(7/8, 1/8, 3/8)",
"(7/8, 5/8, 7/8)",
"(1/8, 7/8, 3/8)",
"(1/8, 3/8, 7/8)",
"(5/8, 7/8, 7/8)",
"(5/8, 3/8, 3/8)",
),
"hkl: h,k,l=4n+2 or h,k,l=4n",
),
"32c": (
0,
(
"(3/8, 3/8, 3/8)",
"(3/8, 7/8, 7/8)",
"(7/8, 3/8, 7/8)",
"(7/8, 7/8, 3/8)",
"(5/8, 1/8, 7/8)",
"(5/8, 5/8, 3/8)",
"(1/8, 1/8, 3/8)",
"(1/8, 5/8, 7/8)",
"(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)",
"(1/8, 3/8, 5/8)",
"(1/8, 7/8, 1/8)",
"(3/8, 1/8, 5/8)",
"(3/8, 5/8, 1/8)",
"(7/8, 1/8, 1/8)",
"(7/8, 5/8, 5/8)",
),
"hkl: h,k,l=4n+2 or h,k,l=4n",
),
"48d": (
0,
(
"(1/4, 0, 0)",
"(1/4, 1/2, 1/2)",
"(3/4, 0, 1/2)",
"(3/4, 1/2, 0)",
"(3/4, 1/2, 1/2)",
"(3/4, 0, 0)",
"(1/4, 1/2, 0)",
"(1/4, 0, 1/2)",
"(0, 1/4, 0)",
"(0, 3/4, 1/2)",
"(1/2, 1/4, 1/2)",
"(1/2, 3/4, 0)",
"(1/2, 3/4, 1/2)",
"(1/2, 1/4, 0)",
"(0, 3/4, 0)",
"(0, 1/4, 1/2)",
"(0, 0, 1/4)",
"(0, 1/2, 3/4)",
"(1/2, 0, 3/4)",
"(1/2, 1/2, 1/4)",
"(1/2, 1/2, 3/4)",
"(1/2, 0, 1/4)",
"(0, 1/2, 1/4)",
"(0, 0, 3/4)",
"(3/4, 1/2, 3/4)",
"(3/4, 0, 1/4)",
"(1/4, 1/2, 1/4)",
"(1/4, 0, 3/4)",
"(1/4, 0, 1/4)",
"(1/4, 1/2, 3/4)",
"(3/4, 0, 3/4)",
"(3/4, 1/2, 1/4)",
"(0, 1/4, 3/4)",
"(0, 3/4, 1/4)",
"(1/2, 1/4, 1/4)",
"(1/2, 3/4, 3/4)",
"(1/2, 3/4, 1/4)",
"(1/2, 1/4, 3/4)",
"(0, 3/4, 3/4)",
"(0, 1/4, 1/4)",
"(3/4, 1/4, 1/2)",
"(3/4, 3/4, 0)",
"(1/4, 1/4, 0)",
"(1/4, 3/4, 1/2)",
"(1/4, 3/4, 0)",
"(1/4, 1/4, 1/2)",
"(3/4, 3/4, 1/2)",
"(3/4, 1/4, 0)",
),
"hkl: h+k+l=4n",
),
"64e": (
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)",
"(-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+1/4)",
"(-x+1/4, -x+1/4, -x+3/4)",
"(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)",
"(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+1/4)",
"(x+3/4, -x+3/4, x+3/4)",
"(-x+1/4, 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, -x+1/2, x)",
"(-x, -x, x+1/2)",
"(-x+1/2, -x+1/2, x+1/2)",
"(-x+1/2, -x, 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, -x)",
"(-x+1/2, x+1/2, -x+1/2)",
"(-x, x, -x+1/2)",
"(-x, x+1/2, -x)",
"(x, -x, -x+1/2)",
"(x, -x+1/2, -x)",
"(x+1/2, -x, -x)",
"(x+1/2, -x+1/2, -x+1/2)",
),
"hkl: h=2n",
),
"96f": (
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)",
"(-x+3/4, 3/4, 3/4)",
"(-x+3/4, 1/4, 1/4)",
"(-x+1/4, 3/4, 1/4)",
"(-x+1/4, 1/4, 3/4)",
"(x+3/4, 1/4, 1/4)",
"(x+3/4, 3/4, 3/4)",
"(x+1/4, 1/4, 3/4)",
"(x+1/4, 3/4, 1/4)",
"(3/4, -x+3/4, 3/4)",
"(3/4, -x+1/4, 1/4)",
"(1/4, -x+3/4, 1/4)",
"(1/4, -x+1/4, 3/4)",
"(1/4, x+3/4, 1/4)",
"(1/4, x+1/4, 3/4)",
"(3/4, x+3/4, 3/4)",
"(3/4, x+1/4, 1/4)",
"(3/4, 3/4, -x+3/4)",
"(3/4, 1/4, -x+1/4)",
"(1/4, 3/4, -x+1/4)",
"(1/4, 1/4, -x+3/4)",
"(1/4, 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)",
"(0, -x+1/2, 0)",
"(0, -x, 1/2)",
"(1/2, -x+1/2, 1/2)",
"(1/2, -x, 0)",
"(1/2, x+1/2, 1/2)",
"(1/2, x, 0)",
"(0, x+1/2, 0)",
"(0, x, 1/2)",
"(-x, 1/2, 0)",
"(-x, 0, 1/2)",
"(-x+1/2, 1/2, 1/2)",
"(-x+1/2, 0, 0)",
"(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",
),
"96g": (
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)",
"(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)",
"(7/8, -y+1/4, -y+1/2)",
"(7/8, -y+3/4, -y)",
"(1/8, y+3/4, -y+1/2)",
"(1/8, y+1/4, -y)",
"(5/8, y+3/4, -y)",
"(5/8, y+1/4, -y+1/2)",
"(y+1/2, 5/8, -y+3/4)",
"(y+1/2, 1/8, -y+1/4)",
"(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)",
"(-y, 3/8, -y+1/4)",
"(-y, 7/8, -y+3/4)",
"(-y+1/2, 3/8, -y+3/4)",
"(-y+1/2, 7/8, -y+1/4)",
"(-y+1/2, 1/8, y+3/4)",
"(-y+1/2, 5/8, y+1/4)",
"(-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,
),
"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, -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)",
"(-x+3/4, -y+3/4, -z+3/4)",
"(-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)",
"(-z+1/4, x+3/4, y+1/4)",
"(-z+1/4, x+1/4, y+3/4)",
"(-z+3/4, x+3/4, y+3/4)",
"(-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, "
"hhl: h,l=2n, h00: h=4n",
),
},
"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)",
"(3/8, 3/8, 3/8)",
"(3/8, 7/8, 7/8)",
"(7/8, 7/8, 7/8)",
"(7/8, 3/8, 3/8)",
"(3/8, 7/8, 3/8)",
"(3/8, 3/8, 7/8)",
"(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",
),
"32b": (
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)",
"(0, 1/2, 3/4)",
"(0, 0, 1/4)",
"(1/2, 1/2, 1/4)",
"(1/2, 0, 3/4)",
"(1/2, 3/4, 0)",
"(1/2, 1/4, 1/2)",
"(0, 3/4, 1/2)",
"(0, 1/4, 0)",
"(3/4, 0, 1/2)",
"(3/4, 1/2, 0)",
"(1/4, 0, 0)",
"(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",
),
"32c": (
0,
(
"(0, 0, 0)",
"(0, 1/2, 1/2)",
"(1/2, 0, 1/2)",
"(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",
),
"48d": (
0,
(
"(7/8, 1/8, 1/8)",
"(7/8, 5/8, 5/8)",
"(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)",
"(7/8, 1/8, 7/8)",
"(7/8, 5/8, 3/8)",
"(3/8, 1/8, 3/8)",
"(3/8, 5/8, 7/8)",
"(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, 7/8)",
"(5/8, 7/8, 3/8)",
"(1/8, 3/8, 3/8)",
"(1/8, 7/8, 7/8)",
"(1/8, 7/8, 3/8)",
"(1/8, 3/8, 7/8)",
"(5/8, 7/8, 7/8)",
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"(3/8, 3/8, 1/8)",
"(7/8, 7/8, 1/8)",
"(7/8, 3/8, 5/8)",
),
"n/a",
),
"64e": (
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)",
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"(x+1/2, x, x)",
"(x, x+1/2, x)",
"(x, x, x+1/2)",
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"(x+1/2, -x+1/4, -x+1/4)",
"(x+1/2, -x+3/4, -x+3/4)",
),
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),
"96f": (
1,
(
"(x, 1/8, 1/8)",
"(x, 5/8, 5/8)",
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"(7/8, x+3/4, 7/8)",
"(7/8, x+1/4, 3/8)",
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"(3/8, 7/8, -x+1/2)",
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"(5/8, 5/8, -x+3/4)",
"(1/8, 1/8, -x+3/4)",
"(1/8, 5/8, -x+1/4)",
),
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),
"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)",
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"(y+1/4, 1/2, y+1/2)",
"(y+1/4, 0, y)",
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"(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)",
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"(y+1/4, y+1/2, 0)",
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"(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)",
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"(z+1/2, -x+1/4, -y+3/4)",
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"(y+1/2, z+1/2, x)",
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"(x+3/4, z+1/4, -y)",
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"(x+3/4, -z, y+1/4)",
"(x+3/4, -z+1/2, y+3/4)",
"(z+3/4, y+1/4, -x)",
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"(z+1/4, y+1/4, -x+1/2)",
"(z+1/4, y+3/4, -x)",
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"(z+3/4, -y, x+1/4)",
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"(-z, y+3/4, x+1/4)",
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"(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",
),
},
}