Symmetry Representation

Space Group Symmetry

In crystallography, the Hermann-Mauguin notation is used to represent the symmetry of a crystal structure. Using this notation, the symmetry of a crystal structure can be described by a space group symbol, which is a combination of letters and numbers that represent the symmetry operations that can be applied to the structure. A full Hermann-Mauguin notation can be broken down into four parts:

1. A single letter (P, A, B, C, I, R) indicating the type of lattice

2. A symbol denoting the symmetry for the primary direction.

3. A symbol denoting the symmetry for the secondary direction.

4. A symbol denoting the symmetry for the tertiary direction.

Symmetry definitions in the Hermann-Mauguin notation.

System	Primary	Secondary	Tertiary	Possible Symmetry Elements
Triclinic	—	—	—	1, -1.
Monoclinic	[010]	—	—	2, 2₁, m, c, 2/m, 2/c, 2₁/c.
Orthorhombic	[100]	[010]	[001]	2, 2₁, m, a, b, c, n, d.
Tetragonal	[001]	[100]/[010]	[110]/[101]/…	4ₙ(/m) @ [001].
Tri/Hexagonal	[001]	[100]/[010]	[110]/[101]/..	3ₙ/6ₙ, -3, -6 @ [001]
Cubic	[100]/…	[111]/[1̄11]/…	[110]/[101]/…	4ₙ @ [100], 3ₙ @ [111], 2ₙ @ [110]

For example, the space group 227 has a symbol of Fd-3m or F 4₁/d -3 2/m in the full Hermann-Mauguin notation. This means it has

1. a face centered unit cell

2. a 4₁/d (including 1, -1, 2₁, d, 4₁, -4) symmetry in the [100] family direction.

3. a -3 (including 1, -1, 3) symmetry in the [111] family directions.

4. a 2/m (including 1, -1, 2, m) symmetry in the [110] family directions.

In most cases, the short Hermann-Mauguin notation is used to describe the symmetry of a crystal structure. For the case of F 4₁/d -3 2/m, it can be simplified to Fd-3m by removing the redundant information due to the following reasons:

• 4₁/d is reduced to d since the primary direction must have the 4-fold,

• 2/m is reduced to m since the tertiary direction must have the 2-fold symmetry.

Similarly, the space group 61 P 2₁/b 2₁/c 2₁/a can be simplified to Pbca since the 2₁ must be present in that particular setting. However, the full Hermann-Mauguin notation is more informative and can be used to describe the symmetry of a crystal structure in more detail.

Below shows the symmetry element analysis of the space group Fd-3m on the 15 high symmetry crystallographic axes.

Symmetry analysis of space group 227 (Fd-3m)

Index	Direction	Symmetry elements	Symbol
0	(1, 0, 0)	1, -1, 2₁, d, 4₁, -4	4₁/d
1	(0, 1, 0)	1, -1, 2₁, d, 4₁, -4	4₁/d
2	(0, 0, 1)	1, -1, 2₁, d, 4₁, -4	4₁/d
3	(1, 1, 1)	1, -1, 3	-3
4	(1, -1, -1)	1, -1, 3	-3
5	(-1, 1, -1)	1, -1, 3	-3
6	(-1, -1, 1)	1, -1, 3	-3
7	(1, -1, 0)	1, -1, 2, m	2/m
8	(1, 1, 0)	1, -1, 2, d	2/d
9	(0, 1, -1)	1, -1, 2, m	2/m
10	(0, 1, 1)	1, -1, 2, d	2/d
11	(-1, 0, 1)	1, -1, 2, m	2/m
12	(1, 0, 1)	1, -1, 2, d	2/d
13	(1, -2, 0)	1, -1	-1
14	(2, -1, 0)	1, -1	-1

One can easily verify this via PyXtal as follows.

from pyxtal.symmetry import Group
spg = Group(227)
ss = spg.get_spg_symmetry_object()
ss.to_beautiful_matrix_representation(skip=False)

>>> Order Axis   1  -1 2  2_1 m  a  b  c  n  d  3  3_1 3_2 4  4_1 4_2 4_3 -4
  0 ( 1  0  0):  1  1  0  1   0  0  0  0  0  1  0  0   0   0  1   0   0   1  # 4_1/d
  0 ( 0  1  0):  1  1  0  1   0  0  0  0  0  1  0  0   0   0  1   0   0   1  # 4_1/d
  0 ( 0  0  1):  1  1  0  1   0  0  0  0  0  1  0  0   0   0  1   0   0   1  # 4_1/d
  1 ( 1  1  1):  1  1  0  0   0  0  0  0  0  0  1  0   0   0  0   0   0   0  # -3
  1 ( 1 -1 -1):  1  1  0  0   0  0  0  0  0  0  1  0   0   0  0   0   0   0  # -3
  1 (-1  1 -1):  1  1  0  0   0  0  0  0  0  0  1  0   0   0  0   0   0   0  # -3
  1 (-1 -1  1):  1  1  0  0   0  0  0  0  0  0  1  0   0   0  0   0   0   0  # -3
  2 ( 1 -1  0):  1  1  1  0   1  0  0  0  0  0  0  0   0   0  0   0   0   0  # 2/m
  2 ( 1  1  0):  1  1  1  0   1  0  0  0  0  0  0  0   0   0  0   0   0   0  # 2/m
  2 ( 0  1 -1):  1  1  1  0   1  0  0  0  0  0  0  0   0   0  0   0   0   0  # 2/m
  2 ( 0  1  1):  1  1  1  0   1  0  0  0  0  0  0  0   0   0  0   0   0   0  # 2/m
  2 (-1  0  1):  1  1  1  0   1  0  0  0  0  0  0  0   0   0  0   0   0   0  # 2/m
  2 ( 1  0  1):  1  1  1  0   1  0  0  0  0  0  0  0   0   0  0   0   0   0  # 2/m

In the above output, we use a 1D 18-length array to represent the symmetry elements (1, -1, 2, 2₁, m, a, b, c, n, d, 3, 3₁, 3₂, 4, 4₁, 4₂, 4₃, -4).

Space Group Symmetry’s Digital Representation

For the application of deep learning, the space group symmetry can be represented as a 14 lattice indices + 15x18 matrix.

For the lattice index, we divde it into 16 possible cases (0-15) as shown below:

ID	Lattice Type
0	Triclinic Primitive
1	Monoclinic Primitive
2	Monoclinic C-Base Centered
3	Orthorhombic Primitive
4	Orthorhombic A-base Centered
5	Orthorhombic B-base Centered
6	Orthorhombic C-base Centered
7	Orthorhombic Body Centered
8	Orthorhombic Face Centered
9	Tetragonal Primitive
10	Tetragonal Body Centered
11	Hexagonal Primitive
12	Hexagonal Rhombehedral
13	Cubic Primitive
14	Cubic Body Centered
15	Cubic Face Centered

For the matrix, the rows represent 15 directions, including

Index	Direction
0	(1, 0, 0)
1	(0, 1, 0)
2	(0, 0, 1)
3	(1, 1, 1)
4	(1, -1, -1)
5	(-1, 1, -1)
6	(-1, -1, 1)
7	(1, -1, 0)
8	(1, 1, 0)
9	(0, 1, -1)
10	(0, 1, 1)
11	(-1, 0, 1)
12	(1, 0, 1)
13	(1, 2, 0)
14	(2, 1, 0)

Ant the columns represent 18 symmetry elements. The value of each element in the matrix indicates the presence (1) or absence (0) of a symmetry operation. There exist a total of 48 combinational symmetries,

Index	Symmetry elements	Symbol
0	1	1
1	1, -1	̄1
2	1, 2	2
3	1, 2₁	2₁
4	1, m	m
5	1, a	a
6	1, b	b
7	1, c	c
8	1, n	n
9	1, d	d
10	1, 3	3
11	1, 3₁	3₁
12	1, 3₂	3₂
13	1, -1, 2, m	2/m
14	1, -1, 2, a	2/a
15	1, -1, 2, b	2/b
16	1, -1, 2, c	2/c
17	1, -1, 2, n	2/n
18	1, -1, 2, d	2/d
19	1, -1, 2₁, m	2₁/m
20	1, -1, 2₁, a	2₁/a
21	1, -1, 2₁, b	2₁/b
22	1, -1, 2₁, c	2₁/c
23	1, -1, 2₁, n	2₁/n
24	1, -1, 2₁, d	2₁/d
25	1, 2, 4	4
26	1, 2₁, 4₁	4₁
27	1, 2, 4₂	4₂
28	1, 2₁, 4₃	4₃
29	1, 2, -4	-4
30	1, -1, 3	-3
31	1, 2, 3	6
32	1, 2₁, 3₁	6₁
33	1, 2₁, 3₂	6₅
34	1, 2, 3₂	6₂
35	1, 2, 3₁	6₄
36	1, 2₁, 3	6₃
37	1, m, 3	-6
38	1, -1, 2, m, 4, -4	4/m
39	1, -1, 2, n, 4, -4	4/n
40	1, -1, 2₁, a, 4₁, -4	4₁/a
41	1, -1, 2₁, b, 4₁, -4	4₁/b
42	1, -1, 2₁, c, 4₁, -4	4₁/c
43	1, -1, 2₁, d, 4₁, -4	4₁/d
44	1, -1, 2, m, 4₂, -4	4₂/m
45	1, -1, 2, m, 4₂, -4	4₂/n
46	1, -1, 2, m, 3	6/m
47	1, -1, 2₁, m, 3	6₃/m

In PyXtal, this representation can be easily obtained via the get_spg_representation() method. The first element of the output is the lattice index, and the second element is a 15x48 matrix representing the symmetry elements.

from pyxtal.symmetry import Group
spg = Group(227)
id, matrix = spg.get_spg_representation()
print(id)
print(matrix)

>>> 13 # lattice id
>>> # one-hot encoding of 15*48 matrix to represent the space group Fd-3m
[[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]])

Wyckoff Site Symmetry

For each space group, the Wyckoff positions are defined by the symmetry of the site. The Wyckoff positions are labeled with a letter and a number, where the letter indicates the type of site and the number indicates the multiplicity of that site. Below, we show the Wyckoff site symmetry for the space group 227 (Fd-3m) as an example.

from pyxtal.symmetry import Group
spg = Group(227)
print(spg)
wp = spg[-1]   # Get the last Wyckoff position 8a
ss.to_beautiful_matrix_representation() # List symmetry elements

>>> -- Spacegroup --# 227 (Fd-3m)--
192i  site symm: 1
96h       site symm: ..2
96g       site symm: ..m
48f       site symm: 2.mm
32e       site symm: .3m
16d       site symm: .-3m
16c       site symm: .-3m
8b        site symm: -43m
8a        site symm: -43m

>>> Order Axis     1    -1   2    m    3    4    -4   -3   6    -6
  0 ( 1  0  0):    1    0    1    0    0    0    1    0    0    0     -4
  0 ( 0  1  0):    1    0    1    0    0    0    1    0    0    0     -4
  0 ( 0  0  1):    1    0    1    0    0    0    1    0    0    0     -4
  1 ( 1  1  1):    1    0    0    0    1    0    0    0    0    0      3
  1 ( 1 -1 -1):    1    0    0    0    1    0    0    0    0    0      3
  1 (-1  1 -1):    1    0    0    0    1    0    0    0    0    0      3
  1 (-1 -1  1):    1    0    0    0    1    0    0    0    0    0      3
  2 ( 1 -1  0):    1    0    0    1    0    0    0    0    0    0      m
  2 ( 1  1  0):    1    0    0    1    0    0    0    0    0    0      m
  2 ( 0  1 -1):    1    0    0    1    0    0    0    0    0    0      m
  2 ( 0  1  1):    1    0    0    1    0    0    0    0    0    0      m
  2 (-1  0  1):    1    0    0    1    0    0    0    0    0    0      m
  2 ( 1  0  1):    1    0    0    1    0    0    0    0    0    0      m

In space group 227, the Wyckoff position 8a indicates that there are 8 equivalent sites in the unit cell, with a site symmetry of -43m. Unlike the Hermann-Mauguin notation, the site symmetry does not count the translation symmetry. Hence, it does not include the screw axis (e.g., 2₁, 3₁, 4₁, 6₁) or glide plane symmetry (a, b, c, n, d). There are 7 fundamental point group symmetries (1, -1, 2, m, 3, 4, 6, -6) and 5 additional compound group symmetries (-3, 6, 2/m, 4/m, 6/m). For 8a in space group 227, its site symmetry -43m includes

1. 4-fold rotation axis (-4) @ [100] family directions,

2. 3-fold rotation axis (3) @ [111] family directions,

3. 2-fold rotation axis (m) @ [110] family directions.

Site Symmetry’s Digital Representation

For the application of deep learning, the Wyckoff site symmetry can be represented as a 15x7 matrix, where the rows and columns represent the symmetry elements. The value of each element in the matrix indicates the presence or absence of a symmetry operation. For example, a value of 1 indicates that the symmetry operation is present, while a value of 0 indicates that it is absent. Given that there exist a total of 13 site symmetries (1, -1, 2, m, 3, 4, 6, -6, -3, 6, 2/m, 4/m, 6/m), it can be further converted to an one-hot encoding format of (15x13) matrix via PyXtal as follows:

from pyxtal.symmetry import Group
spg = Group(227)
rep = wp.get_site_symmetry_object().to_one_hot()

>>> # one-hot encoding of the 8a site symmetry of space group 227
[[1 0 0 0 0 0 0 0 0 0 0 0 0]
 [1 0 0 0 0 0 0 0 0 0 0 0 0]
 [1 0 0 0 0 0 0 0 0 0 0 0 0]
 [0 1 0 0 0 0 0 0 0 0 0 0 0]
 [0 1 0 0 0 0 0 0 0 0 0 0 0]
 [0 1 0 0 0 0 0 0 0 0 0 0 0]
 [0 1 0 0 0 0 0 0 0 0 0 0 0]
 [0 0 1 0 0 0 0 0 0 0 0 0 0]
 [0 0 1 0 0 0 0 0 0 0 0 0 0]
 [0 0 1 0 0 0 0 0 0 0 0 0 0]
 [0 0 1 0 0 0 0 0 0 0 0 0 0]
 [0 0 1 0 0 0 0 0 0 0 0 0 0]
 [0 0 1 0 0 0 0 0 0 0 0 0 0]
 [1 0 0 0 0 0 0 0 0 0 0 0 0]
 [1 0 0 0 0 0 0 0 0 0 0 0 0]]

Complete list of Wyckoff Site Symmetry Table

Using PyXtal, you can easily access the Wyckoff site symmetry for all 230 space groups as follows:

from pyxtal.symmetry import Group
for g in range(1, 231):
    spg = Group(g)
    for wp in spg:
        wp.get_site_symmetry()
        print(spg.number, spg.symbol, wp.get_label(), wp.site_symm)

The following table lists the space group number, symbol, Wyckoff label, and site symmetry for all 230 space groups.

Space Group Number	Space Group Symbol	Wyckoff Label	Site Symmetry
1	P1	1a	1
2	P-1	2i	1
2	P-1	1h	-1
2	P-1	1g	-1
2	P-1	1f	-1
2	P-1	1e	-1
2	P-1	1d	-1
2	P-1	1c	-1
2	P-1	1b	-1
2	P-1	1a	-1
3	P2	2e	1
3	P2	1d	2
3	P2	1c	2
3	P2	1b	2
3	P2	1a	2
4	P21	2a	1
5	C2	4c	1
5	C2	2b	2
5	C2	2a	2
6	Pm	2c	1
6	Pm	1b	m
6	Pm	1a	m
7	Pc	2a	1
8	Cm	4b	1
8	Cm	2a	m
9	Cc	4a	1
10	P2/m	4o	1
10	P2/m	2n	m
10	P2/m	2m	m
10	P2/m	2l	2
10	P2/m	2k	2
10	P2/m	2j	2
10	P2/m	2i	2
10	P2/m	1h	2/m
10	P2/m	1g	2/m
10	P2/m	1f	2/m
10	P2/m	1e	2/m
10	P2/m	1d	2/m
10	P2/m	1c	2/m
10	P2/m	1b	2/m
10	P2/m	1a	2/m
11	P21/m	4f	1
11	P21/m	2e	m
11	P21/m	2d	-1
11	P21/m	2c	-1
11	P21/m	2b	-1
11	P21/m	2a	-1
12	C2/m	8j	1
12	C2/m	4i	m
12	C2/m	4h	2
12	C2/m	4g	2
12	C2/m	4f	-1
12	C2/m	4e	-1
12	C2/m	2d	2/m
12	C2/m	2c	2/m
12	C2/m	2b	2/m
12	C2/m	2a	2/m
13	P2/c	4g	1
13	P2/c	2f	2
13	P2/c	2e	2
13	P2/c	2d	-1
13	P2/c	2c	-1
13	P2/c	2b	-1
13	P2/c	2a	-1
14	P21/c	4e	1
14	P21/c	2d	-1
14	P21/c	2c	-1
14	P21/c	2b	-1
14	P21/c	2a	-1
15	C2/c	8f	1
15	C2/c	4e	2
15	C2/c	4d	-1
15	C2/c	4c	-1
15	C2/c	4b	-1
15	C2/c	4a	-1
16	P222	4u	1
16	P222	2t	..2
16	P222	2s	..2
16	P222	2r	..2
16	P222	2q	..2
16	P222	2p	.2.
16	P222	2o	.2.
16	P222	2n	.2.
16	P222	2m	.2.
16	P222	2l	2..
16	P222	2k	2..
16	P222	2j	2..
16	P222	2i	2..
16	P222	1h	222
16	P222	1g	222
16	P222	1f	222
16	P222	1e	222
16	P222	1d	222
16	P222	1c	222
16	P222	1b	222
16	P222	1a	222
17	P2221	4e	1
17	P2221	2d	.2.
17	P2221	2c	.2.
17	P2221	2b	2..
17	P2221	2a	2..
18	P21212	4c	1
18	P21212	2b	..2
18	P21212	2a	..2
19	P212121	4a	1
20	C2221	8c	1
20	C2221	4b	.2.
20	C2221	4a	2..
21	C222	8l	1
21	C222	4k	..2
21	C222	4j	..2
21	C222	4i	..2
21	C222	4h	.2.
21	C222	4g	.2.
21	C222	4f	2..
21	C222	4e	2..
21	C222	2d	222
21	C222	2c	222
21	C222	2b	222
21	C222	2a	222
22	F222	16k	1
22	F222	8j	2..
22	F222	8i	.2.
22	F222	8h	..2
22	F222	8g	..2
22	F222	8f	.2.
22	F222	8e	2..
22	F222	4d	222
22	F222	4c	222
22	F222	4b	222
22	F222	4a	222
23	I222	8k	1
23	I222	4j	..2
23	I222	4i	..2
23	I222	4h	.2.
23	I222	4g	.2.
23	I222	4f	2..
23	I222	4e	2..
23	I222	2d	222
23	I222	2c	222
23	I222	2b	222
23	I222	2a	222
24	I212121	8d	1
24	I212121	4c	..2
24	I212121	4b	.2.
24	I212121	4a	2..
25	Pmm2	4i	1
25	Pmm2	2h	m..
25	Pmm2	2g	m..
25	Pmm2	2f	.m.
25	Pmm2	2e	.m.
25	Pmm2	1d	mm2
25	Pmm2	1c	mm2
25	Pmm2	1b	mm2
25	Pmm2	1a	mm2
26	Pmc21	4c	1
26	Pmc21	2b	m..
26	Pmc21	2a	m..
27	Pcc2	4e	1
27	Pcc2	2d	..2
27	Pcc2	2c	..2
27	Pcc2	2b	..2
27	Pcc2	2a	..2
28	Pma2	4d	1
28	Pma2	2c	m..
28	Pma2	2b	..2
28	Pma2	2a	..2
29	Pca21	4a	1
30	Pnc2	4c	1
30	Pnc2	2b	..2
30	Pnc2	2a	..2
31	Pmn21	4b	1
31	Pmn21	2a	m..
32	Pba2	4c	1
32	Pba2	2b	..2
32	Pba2	2a	..2
33	Pna21	4a	1
34	Pnn2	4c	1
34	Pnn2	2b	..2
34	Pnn2	2a	..2
35	Cmm2	8f	1
35	Cmm2	4e	m..
35	Cmm2	4d	.m.
35	Cmm2	4c	..2
35	Cmm2	2b	mm2
35	Cmm2	2a	mm2
36	Cmc21	8b	1
36	Cmc21	4a	m..
37	Ccc2	8d	1
37	Ccc2	4c	..2
37	Ccc2	4b	..2
37	Ccc2	4a	..2
38	Amm2	8f	1
38	Amm2	4e	m..
38	Amm2	4d	m..
38	Amm2	4c	.m.
38	Amm2	2b	mm2
38	Amm2	2a	mm2
39	Aem2	8d	1
39	Aem2	4c	.m.
39	Aem2	4b	..2
39	Aem2	4a	..2
40	Ama2	8c	1
40	Ama2	4b	m..
40	Ama2	4a	..2
41	Aea2	8b	1
41	Aea2	4a	..2
42	Fmm2	16e	1
42	Fmm2	8d	.m.
42	Fmm2	8c	m..
42	Fmm2	8b	..2
42	Fmm2	4a	mm2
43	Fdd2	16b	1
43	Fdd2	8a	..2
44	Imm2	8e	1
44	Imm2	4d	m..
44	Imm2	4c	.m.
44	Imm2	2b	mm2
44	Imm2	2a	mm2
45	Iba2	8c	1
45	Iba2	4b	..2
45	Iba2	4a	..2
46	Ima2	8c	1
46	Ima2	4b	m..
46	Ima2	4a	..2
47	Pmmm	8A	1
47	Pmmm	4z	..m
47	Pmmm	4y	..m
47	Pmmm	4x	.m.
47	Pmmm	4w	.m.
47	Pmmm	4v	m..
47	Pmmm	4u	m..
47	Pmmm	2t	mm2
47	Pmmm	2s	mm2
47	Pmmm	2r	mm2
47	Pmmm	2q	mm2
47	Pmmm	2p	m2m
47	Pmmm	2o	m2m
47	Pmmm	2n	m2m
47	Pmmm	2m	m2m
47	Pmmm	2l	2mm
47	Pmmm	2k	2mm
47	Pmmm	2j	2mm
47	Pmmm	2i	2mm
47	Pmmm	1h	mmm
47	Pmmm	1g	mmm
47	Pmmm	1f	mmm
47	Pmmm	1e	mmm
47	Pmmm	1d	mmm
47	Pmmm	1c	mmm
47	Pmmm	1b	mmm
47	Pmmm	1a	mmm
48	Pnnn	8m	1
48	Pnnn	4l	..2
48	Pnnn	4k	..2
48	Pnnn	4j	.2.
48	Pnnn	4i	.2.
48	Pnnn	4h	2..
48	Pnnn	4g	2..
48	Pnnn	4f	-1
48	Pnnn	4e	-1
48	Pnnn	2d	222
48	Pnnn	2c	222
48	Pnnn	2b	222
48	Pnnn	2a	222
49	Pccm	8r	1
49	Pccm	4q	..m
49	Pccm	4p	..2
49	Pccm	4o	..2
49	Pccm	4n	..2
49	Pccm	4m	..2
49	Pccm	4l	.2.
49	Pccm	4k	.2.
49	Pccm	4j	2..
49	Pccm	4i	2..
49	Pccm	2h	222
49	Pccm	2g	222
49	Pccm	2f	222
49	Pccm	2e	222
49	Pccm	2d	..2/m
49	Pccm	2c	..2/m
49	Pccm	2b	..2/m
49	Pccm	2a	..2/m
50	Pban	8m	1
50	Pban	4l	..2
50	Pban	4k	..2
50	Pban	4j	.2.
50	Pban	4i	.2.
50	Pban	4h	2..
50	Pban	4g	2..
50	Pban	4f	-1
50	Pban	4e	-1
50	Pban	2d	222
50	Pban	2c	222
50	Pban	2b	222
50	Pban	2a	222
51	Pmma	8l	1
51	Pmma	4k	m..
51	Pmma	4j	.m.
51	Pmma	4i	.m.
51	Pmma	4h	.2.
51	Pmma	4g	.2.
51	Pmma	2f	mm2
51	Pmma	2e	mm2
51	Pmma	2d	.2/m.
51	Pmma	2c	.2/m.
51	Pmma	2b	.2/m.
51	Pmma	2a	.2/m.
52	Pnna	8e	1
52	Pnna	4d	2..
52	Pnna	4c	..2
52	Pnna	4b	-1
52	Pnna	4a	-1
53	Pmna	8i	1
53	Pmna	4h	m..
53	Pmna	4g	.2.
53	Pmna	4f	2..
53	Pmna	4e	2..
53	Pmna	2d	2/m..
53	Pmna	2c	2/m..
53	Pmna	2b	2/m..
53	Pmna	2a	2/m..
54	Pcca	8f	1
54	Pcca	4e	..2
54	Pcca	4d	..2
54	Pcca	4c	.2.
54	Pcca	4b	-1
54	Pcca	4a	-1
55	Pbam	8i	1
55	Pbam	4h	..m
55	Pbam	4g	..m
55	Pbam	4f	..2
55	Pbam	4e	..2
55	Pbam	2d	..2/m
55	Pbam	2c	..2/m
55	Pbam	2b	..2/m
55	Pbam	2a	..2/m
56	Pccn	8e	1
56	Pccn	4d	..2
56	Pccn	4c	..2
56	Pccn	4b	-1
56	Pccn	4a	-1
57	Pbcm	8e	1
57	Pbcm	4d	..m
57	Pbcm	4c	2..
57	Pbcm	4b	-1
57	Pbcm	4a	-1
58	Pnnm	8h	1
58	Pnnm	4g	..m
58	Pnnm	4f	..2
58	Pnnm	4e	..2
58	Pnnm	2d	..2/m
58	Pnnm	2c	..2/m
58	Pnnm	2b	..2/m
58	Pnnm	2a	..2/m
59	Pmmn	8g	1
59	Pmmn	4f	.m.
59	Pmmn	4e	m..
59	Pmmn	4d	-1
59	Pmmn	4c	-1
59	Pmmn	2b	mm2
59	Pmmn	2a	mm2
60	Pbcn	8d	1
60	Pbcn	4c	.2.
60	Pbcn	4b	-1
60	Pbcn	4a	-1
61	Pbca	8c	1
61	Pbca	4b	-1
61	Pbca	4a	-1
62	Pnma	8d	1
62	Pnma	4c	.m.
62	Pnma	4b	-1
62	Pnma	4a	-1
63	Cmcm	16h	1
63	Cmcm	8g	..m
63	Cmcm	8f	m..
63	Cmcm	8e	2..
63	Cmcm	8d	-1
63	Cmcm	4c	m2m
63	Cmcm	4b	2/m..
63	Cmcm	4a	2/m..
64	Cmce	16g	1
64	Cmce	8f	m..
64	Cmce	8e	.2.
64	Cmce	8d	2..
64	Cmce	8c	-1
64	Cmce	4b	2/m..
64	Cmce	4a	2/m..
65	Cmmm	16r	1
65	Cmmm	8q	..m
65	Cmmm	8p	..m
65	Cmmm	8o	.m.
65	Cmmm	8n	m..
65	Cmmm	8m	..2
65	Cmmm	4l	mm2
65	Cmmm	4k	mm2
65	Cmmm	4j	m2m
65	Cmmm	4i	m2m
65	Cmmm	4h	2mm
65	Cmmm	4g	2mm
65	Cmmm	4f	..2/m
65	Cmmm	4e	..2/m
65	Cmmm	2d	mmm
65	Cmmm	2c	mmm
65	Cmmm	2b	mmm
65	Cmmm	2a	mmm
66	Cccm	16m	1
66	Cccm	8l	..m
66	Cccm	8k	..2
66	Cccm	8j	..2
66	Cccm	8i	..2
66	Cccm	8h	.2.
66	Cccm	8g	2..
66	Cccm	4f	..2/m
66	Cccm	4e	..2/m
66	Cccm	4d	..2/m
66	Cccm	4c	..2/m
66	Cccm	4b	222
66	Cccm	4a	222
67	Cmme	16o	1
67	Cmme	8n	.m.
67	Cmme	8m	m..
67	Cmme	8l	..2
67	Cmme	8k	.2.
67	Cmme	8j	.2.
67	Cmme	8i	2..
67	Cmme	8h	2..
67	Cmme	4g	mm2
67	Cmme	4f	.2/m.
67	Cmme	4e	.2/m.
67	Cmme	4d	2/m..
67	Cmme	4c	2/m..
67	Cmme	4b	222
67	Cmme	4a	222
68	Ccce	16i	1
68	Ccce	8h	..2
68	Ccce	8g	..2
68	Ccce	8f	.2.
68	Ccce	8e	2..
68	Ccce	8d	-1
68	Ccce	8c	-1
68	Ccce	4b	222
68	Ccce	4a	222
69	Fmmm	32p	1
69	Fmmm	16o	..m
69	Fmmm	16n	.m.
69	Fmmm	16m	m..
69	Fmmm	16l	2..
69	Fmmm	16k	.2.
69	Fmmm	16j	..2
69	Fmmm	8i	mm2
69	Fmmm	8h	m2m
69	Fmmm	8g	2mm
69	Fmmm	8f	222
69	Fmmm	8e	..2/m
69	Fmmm	8d	.2/m.
69	Fmmm	8c	2/m..
69	Fmmm	4b	mmm
69	Fmmm	4a	mmm
70	Fddd	32h	1
70	Fddd	16g	..2
70	Fddd	16f	.2.
70	Fddd	16e	2..
70	Fddd	16d	-1
70	Fddd	16c	-1
70	Fddd	8b	222
70	Fddd	8a	222
71	Immm	16o	1
71	Immm	8n	..m
71	Immm	8m	.m.
71	Immm	8l	m..
71	Immm	8k	-1
71	Immm	4j	mm2
71	Immm	4i	mm2
71	Immm	4h	m2m
71	Immm	4g	m2m
71	Immm	4f	2mm
71	Immm	4e	2mm
71	Immm	2d	mmm
71	Immm	2c	mmm
71	Immm	2b	mmm
71	Immm	2a	mmm
72	Ibam	16k	1
72	Ibam	8j	..m
72	Ibam	8i	..2
72	Ibam	8h	..2
72	Ibam	8g	.2.
72	Ibam	8f	2..
72	Ibam	8e	-1
72	Ibam	4d	..2/m
72	Ibam	4c	..2/m
72	Ibam	4b	222
72	Ibam	4a	222
73	Ibca	16f	1
73	Ibca	8e	..2
73	Ibca	8d	.2.
73	Ibca	8c	2..
73	Ibca	8b	-1
73	Ibca	8a	-1
74	Imma	16j	1
74	Imma	8i	.m.
74	Imma	8h	m..
74	Imma	8g	.2.
74	Imma	8f	2..
74	Imma	4e	mm2
74	Imma	4d	.2/m.
74	Imma	4c	.2/m.
74	Imma	4b	2/m..
74	Imma	4a	2/m..
75	P4	4d	1
75	P4	2c	2..
75	P4	1b	4..
75	P4	1a	4..
76	P41	4a	1
77	P42	4d	1
77	P42	2c	2..
77	P42	2b	2..
77	P42	2a	2..
78	P43	4a	1
79	I4	8c	1
79	I4	4b	2..
79	I4	2a	4..
80	I41	8b	1
80	I41	4a	2..
81	P-4	4h	1
81	P-4	2g	2..
81	P-4	2f	2..
81	P-4	2e	2..
81	P-4	1d	-4..
81	P-4	1c	-4..
81	P-4	1b	-4..
81	P-4	1a	-4..
82	I-4	8g	1
82	I-4	4f	2..
82	I-4	4e	2..
82	I-4	2d	-4..
82	I-4	2c	-4..
82	I-4	2b	-4..
82	I-4	2a	-4..
83	P4/m	8l	1
83	P4/m	4k	m..
83	P4/m	4j	m..
83	P4/m	4i	2..
83	P4/m	2h	4..
83	P4/m	2g	4..
83	P4/m	2f	2/m..
83	P4/m	2e	2/m..
83	P4/m	1d	4/m..
83	P4/m	1c	4/m..
83	P4/m	1b	4/m..
83	P4/m	1a	4/m..
84	P42/m	8k	1
84	P42/m	4j	m..
84	P42/m	4i	2..
84	P42/m	4h	2..
84	P42/m	4g	2..
84	P42/m	2f	-4..
84	P42/m	2e	-4..
84	P42/m	2d	2/m..
84	P42/m	2c	2/m..
84	P42/m	2b	2/m..
84	P42/m	2a	2/m..
85	P4/n	8g	1
85	P4/n	4f	2..
85	P4/n	4e	-1
85	P4/n	4d	-1
85	P4/n	2c	4..
85	P4/n	2b	-4..
85	P4/n	2a	-4..
86	P42/n	8g	1
86	P42/n	4f	2..
86	P42/n	4e	2..
86	P42/n	4d	-1
86	P42/n	4c	-1
86	P42/n	2b	-4..
86	P42/n	2a	-4..
87	I4/m	16i	1
87	I4/m	8h	m..
87	I4/m	8g	2..
87	I4/m	8f	-1
87	I4/m	4e	4..
87	I4/m	4d	-4..
87	I4/m	4c	2/m..
87	I4/m	2b	4/m..
87	I4/m	2a	4/m..
88	I41/a	16f	1
88	I41/a	8e	2..
88	I41/a	8d	-1
88	I41/a	8c	-1
88	I41/a	4b	-4..
88	I41/a	4a	-4..
89	P422	8p	1
89	P422	4o	.2.
89	P422	4n	.2.
89	P422	4m	.2.
89	P422	4l	.2.
89	P422	4k	..2
89	P422	4j	..2
89	P422	4i	2..
89	P422	2h	4..
89	P422	2g	4..
89	P422	2f	222.
89	P422	2e	222.
89	P422	1d	422
89	P422	1c	422
89	P422	1b	422
89	P422	1a	422
90	P4212	8g	1
90	P4212	4f	..2
90	P4212	4e	..2
90	P4212	4d	2..
90	P4212	2c	4..
90	P4212	2b	2.22
90	P4212	2a	2.22
91	P4122	8d	1
91	P4122	4c	..2
91	P4122	4b	.2.
91	P4122	4a	.2.
92	P41212	8b	1
92	P41212	4a	..2
93	P4222	8p	1
93	P4222	4o	..2
93	P4222	4n	..2
93	P4222	4m	.2.
93	P4222	4l	.2.
93	P4222	4k	.2.
93	P4222	4j	.2.
93	P4222	4i	2..
93	P4222	4h	2..
93	P4222	4g	2..
93	P4222	2f	2.22
93	P4222	2e	2.22
93	P4222	2d	222.
93	P4222	2c	222.
93	P4222	2b	222.
93	P4222	2a	222.
94	P42212	8g	1
94	P42212	4f	..2
94	P42212	4e	..2
94	P42212	4d	2..
94	P42212	4c	2..
94	P42212	2b	2.22
94	P42212	2a	2.22
95	P4322	8d	1
95	P4322	4c	..2
95	P4322	4b	.2.
95	P4322	4a	.2.
96	P43212	8b	1
96	P43212	4a	..2
97	I422	16k	1
97	I422	8j	..2
97	I422	8i	.2.
97	I422	8h	.2.
97	I422	8g	..2
97	I422	8f	2..
97	I422	4e	4..
97	I422	4d	2.22
97	I422	4c	222.
97	I422	2b	422
97	I422	2a	422
98	I4122	16g	1
98	I4122	8f	.2.
98	I4122	8e	..2
98	I4122	8d	..2
98	I4122	8c	2..
98	I4122	4b	2.22
98	I4122	4a	2.22
99	P4mm	8g	1
99	P4mm	4f	.m.
99	P4mm	4e	.m.
99	P4mm	4d	..m
99	P4mm	2c	2mm.
99	P4mm	1b	4mm
99	P4mm	1a	4mm
100	P4bm	8d	1
100	P4bm	4c	..m
100	P4bm	2b	2.mm
100	P4bm	2a	4..
101	P42cm	8e	1
101	P42cm	4d	..m
101	P42cm	4c	2..
101	P42cm	2b	2.mm
101	P42cm	2a	2.mm
102	P42nm	8d	1
102	P42nm	4c	..m
102	P42nm	4b	2..
102	P42nm	2a	2.mm
103	P4cc	8d	1
103	P4cc	4c	2..
103	P4cc	2b	4..
103	P4cc	2a	4..
104	P4nc	8c	1
104	P4nc	4b	2..
104	P4nc	2a	4..
105	P42mc	8f	1
105	P42mc	4e	.m.
105	P42mc	4d	.m.
105	P42mc	2c	2mm.
105	P42mc	2b	2mm.
105	P42mc	2a	2mm.
106	P42bc	8c	1
106	P42bc	4b	2..
106	P42bc	4a	2..
107	I4mm	16e	1
107	I4mm	8d	.m.
107	I4mm	8c	..m
107	I4mm	4b	2mm.
107	I4mm	2a	4mm
108	I4cm	16d	1
108	I4cm	8c	..m
108	I4cm	4b	2.mm
108	I4cm	4a	4..
109	I41md	16c	1
109	I41md	8b	.m.
109	I41md	4a	2mm.
110	I41cd	16b	1
110	I41cd	8a	2..
111	P-42m	8o	1
111	P-42m	4n	..m
111	P-42m	4m	2..
111	P-42m	4l	.2.
111	P-42m	4k	.2.
111	P-42m	4j	.2.
111	P-42m	4i	.2.
111	P-42m	2h	2.mm
111	P-42m	2g	2.mm
111	P-42m	2f	222.
111	P-42m	2e	222.
111	P-42m	1d	-42m
111	P-42m	1c	-42m
111	P-42m	1b	-42m
111	P-42m	1a	-42m
112	P-42c	8n	1
112	P-42c	4m	2..
112	P-42c	4l	2..
112	P-42c	4k	2..
112	P-42c	4j	.2.
112	P-42c	4i	.2.
112	P-42c	4h	.2.
112	P-42c	4g	.2.
112	P-42c	2f	-4..
112	P-42c	2e	-4..
112	P-42c	2d	222.
112	P-42c	2c	222.
112	P-42c	2b	222.
112	P-42c	2a	222.
113	P-421m	8f	1
113	P-421m	4e	..m
113	P-421m	4d	2..
113	P-421m	2c	2.mm
113	P-421m	2b	-4..
113	P-421m	2a	-4..
114	P-421c	8e	1
114	P-421c	4d	2..
114	P-421c	4c	2..
114	P-421c	2b	-4..
114	P-421c	2a	-4..
115	P-4m2	8l	1
115	P-4m2	4k	.m.
115	P-4m2	4j	.m.
115	P-4m2	4i	..2
115	P-4m2	4h	..2
115	P-4m2	2g	2mm.
115	P-4m2	2f	2mm.
115	P-4m2	2e	2mm.
115	P-4m2	1d	-4m2
115	P-4m2	1c	-4m2
115	P-4m2	1b	-4m2
115	P-4m2	1a	-4m2
116	P-4c2	8j	1
116	P-4c2	4i	2..
116	P-4c2	4h	2..
116	P-4c2	4g	2..
116	P-4c2	4f	..2
116	P-4c2	4e	..2
116	P-4c2	2d	-4..
116	P-4c2	2c	-4..
116	P-4c2	2b	2.22
116	P-4c2	2a	2.22
117	P-4b2	8i	1
117	P-4b2	4h	..2
117	P-4b2	4g	..2
117	P-4b2	4f	2..
117	P-4b2	4e	2..
117	P-4b2	2d	2.22
117	P-4b2	2c	2.22
117	P-4b2	2b	-4..
117	P-4b2	2a	-4..
118	P-4n2	8i	1
118	P-4n2	4h	2..
118	P-4n2	4g	..2
118	P-4n2	4f	..2
118	P-4n2	4e	2..
118	P-4n2	2d	2.22
118	P-4n2	2c	2.22
118	P-4n2	2b	-4..
118	P-4n2	2a	-4..
119	I-4m2	16j	1
119	I-4m2	8i	.m.
119	I-4m2	8h	..2
119	I-4m2	8g	..2
119	I-4m2	4f	2mm.
119	I-4m2	4e	2mm.
119	I-4m2	2d	-4m2
119	I-4m2	2c	-4m2
119	I-4m2	2b	-4m2
119	I-4m2	2a	-4m2
120	I-4c2	16i	1
120	I-4c2	8h	..2
120	I-4c2	8g	2..
120	I-4c2	8f	2..
120	I-4c2	8e	..2
120	I-4c2	4d	2.22
120	I-4c2	4c	-4..
120	I-4c2	4b	-4..
120	I-4c2	4a	2.22
121	I-42m	16j	1
121	I-42m	8i	..m
121	I-42m	8h	2..
121	I-42m	8g	.2.
121	I-42m	8f	.2.
121	I-42m	4e	2.mm
121	I-42m	4d	-4..
121	I-42m	4c	222.
121	I-42m	2b	-42m
121	I-42m	2a	-42m
122	I-42d	16e	1
122	I-42d	8d	.2.
122	I-42d	8c	2..
122	I-42d	4b	-4..
122	I-42d	4a	-4..
123	P4/mmm	16u	1
123	P4/mmm	8t	.m.
123	P4/mmm	8s	.m.
123	P4/mmm	8r	..m
123	P4/mmm	8q	m..
123	P4/mmm	8p	m..
123	P4/mmm	4o	m2m.
123	P4/mmm	4n	m2m.
123	P4/mmm	4m	m2m.
123	P4/mmm	4l	m2m.
123	P4/mmm	4k	m.2m
123	P4/mmm	4j	m.2m
123	P4/mmm	4i	2mm.
123	P4/mmm	2h	4mm
123	P4/mmm	2g	4mm
123	P4/mmm	2f	mmm.
123	P4/mmm	2e	mmm.
123	P4/mmm	1d	4/mmm
123	P4/mmm	1c	4/mmm
123	P4/mmm	1b	4/mmm
123	P4/mmm	1a	4/mmm
124	P4/mcc	16n	1
124	P4/mcc	8m	m..
124	P4/mcc	8l	.2.
124	P4/mcc	8k	.2.
124	P4/mcc	8j	..2
124	P4/mcc	8i	2..
124	P4/mcc	4h	4..
124	P4/mcc	4g	4..
124	P4/mcc	4f	222.
124	P4/mcc	4e	2/m..
124	P4/mcc	2d	4/m..
124	P4/mcc	2c	422
124	P4/mcc	2b	4/m..
124	P4/mcc	2a	422
125	P4/nbm	16n	1
125	P4/nbm	8m	..m
125	P4/nbm	8l	.2.
125	P4/nbm	8k	.2.
125	P4/nbm	8j	..2
125	P4/nbm	8i	..2
125	P4/nbm	4h	2.mm
125	P4/nbm	4g	4..
125	P4/nbm	4f	..2/m
125	P4/nbm	4e	..2/m
125	P4/nbm	2d	-42m
125	P4/nbm	2c	-42m
125	P4/nbm	2b	422
125	P4/nbm	2a	422
126	P4/nnc	16k	1
126	P4/nnc	8j	.2.
126	P4/nnc	8i	.2.
126	P4/nnc	8h	..2
126	P4/nnc	8g	2..
126	P4/nnc	8f	-1
126	P4/nnc	4e	4..
126	P4/nnc	4d	-4..
126	P4/nnc	4c	222.
126	P4/nnc	2b	422
126	P4/nnc	2a	422
127	P4/mbm	16l	1
127	P4/mbm	8k	..m
127	P4/mbm	8j	m..
127	P4/mbm	8i	m..
127	P4/mbm	4h	m.2m
127	P4/mbm	4g	m.2m
127	P4/mbm	4f	2.mm
127	P4/mbm	4e	4..
127	P4/mbm	2d	m.mm
127	P4/mbm	2c	m.mm
127	P4/mbm	2b	4/m..
127	P4/mbm	2a	4/m..
128	P4/mnc	16i	1
128	P4/mnc	8h	m..
128	P4/mnc	8g	..2
128	P4/mnc	8f	2..
128	P4/mnc	4e	4..
128	P4/mnc	4d	2.22
128	P4/mnc	4c	2/m..
128	P4/mnc	2b	4/m..
128	P4/mnc	2a	4/m..
129	P4/nmm	16k	1
129	P4/nmm	8j	..m
129	P4/nmm	8i	.m.
129	P4/nmm	8h	..2
129	P4/nmm	8g	..2
129	P4/nmm	4f	2mm.
129	P4/nmm	4e	..2/m
129	P4/nmm	4d	..2/m
129	P4/nmm	2c	4mm
129	P4/nmm	2b	-4m2
129	P4/nmm	2a	-4m2
130	P4/ncc	16g	1
130	P4/ncc	8f	..2
130	P4/ncc	8e	2..
130	P4/ncc	8d	-1
130	P4/ncc	4c	4..
130	P4/ncc	4b	-4..
130	P4/ncc	4a	2.22
131	P42/mmc	16r	1
131	P42/mmc	8q	m..
131	P42/mmc	8p	.m.
131	P42/mmc	8o	.m.
131	P42/mmc	8n	..2
131	P42/mmc	4m	m2m.
131	P42/mmc	4l	m2m.
131	P42/mmc	4k	m2m.
131	P42/mmc	4j	m2m.
131	P42/mmc	4i	2mm.
131	P42/mmc	4h	2mm.
131	P42/mmc	4g	2mm.
131	P42/mmc	2f	-4m2
131	P42/mmc	2e	-4m2
131	P42/mmc	2d	mmm.
131	P42/mmc	2c	mmm.
131	P42/mmc	2b	mmm.
131	P42/mmc	2a	mmm.
132	P42/mcm	16p	1
132	P42/mcm	8o	..m
132	P42/mcm	8n	m..
132	P42/mcm	8m	.2.
132	P42/mcm	8l	.2.
132	P42/mcm	8k	2..
132	P42/mcm	4j	m.2m
132	P42/mcm	4i	m.2m
132	P42/mcm	4h	2.mm
132	P42/mcm	4g	2.mm
132	P42/mcm	4f	2/m..
132	P42/mcm	4e	222.
132	P42/mcm	2d	-42m
132	P42/mcm	2c	m.mm
132	P42/mcm	2b	-42m
132	P42/mcm	2a	m.mm
133	P42/nbc	16k	1
133	P42/nbc	8j	..2
133	P42/nbc	8i	.2.
133	P42/nbc	8h	.2.
133	P42/nbc	8g	2..
133	P42/nbc	8f	2..
133	P42/nbc	8e	-1
133	P42/nbc	4d	-4..
133	P42/nbc	4c	2.22
133	P42/nbc	4b	222.
133	P42/nbc	4a	222.
134	P42/nnm	16n	1
134	P42/nnm	8m	..m
134	P42/nnm	8l	..2
134	P42/nnm	8k	..2
134	P42/nnm	8j	.2.
134	P42/nnm	8i	.2.
134	P42/nnm	8h	2..
134	P42/nnm	4g	2.mm
134	P42/nnm	4f	..2/m
134	P42/nnm	4e	..2/m
134	P42/nnm	4d	2.22
134	P42/nnm	4c	222.
134	P42/nnm	2b	-42m
134	P42/nnm	2a	-42m
135	P42/mbc	16i	1
135	P42/mbc	8h	m..
135	P42/mbc	8g	..2
135	P42/mbc	8f	2..
135	P42/mbc	8e	2..
135	P42/mbc	4d	2.22
135	P42/mbc	4c	2/m..
135	P42/mbc	4b	-4..
135	P42/mbc	4a	2/m..
136	P42/mnm	16k	1
136	P42/mnm	8j	..m
136	P42/mnm	8i	m..
136	P42/mnm	8h	2..
136	P42/mnm	4g	m.2m
136	P42/mnm	4f	m.2m
136	P42/mnm	4e	2.mm
136	P42/mnm	4d	-4..
136	P42/mnm	4c	2/m..
136	P42/mnm	2b	m.mm
136	P42/mnm	2a	m.mm
137	P42/nmc	16h	1
137	P42/nmc	8g	.m.
137	P42/nmc	8f	..2
137	P42/nmc	8e	-1
137	P42/nmc	4d	2mm.
137	P42/nmc	4c	2mm.
137	P42/nmc	2b	-4m2
137	P42/nmc	2a	-4m2
138	P42/ncm	16j	1
138	P42/ncm	8i	..m
138	P42/ncm	8h	..2
138	P42/ncm	8g	..2
138	P42/ncm	8f	2..
138	P42/ncm	4e	2.mm
138	P42/ncm	4d	..2/m
138	P42/ncm	4c	..2/m
138	P42/ncm	4b	-4..
138	P42/ncm	4a	2.22
139	I4/mmm	32o	1
139	I4/mmm	16n	.m.
139	I4/mmm	16m	..m
139	I4/mmm	16l	m..
139	I4/mmm	16k	..2
139	I4/mmm	8j	m2m.
139	I4/mmm	8i	m2m.
139	I4/mmm	8h	m.2m
139	I4/mmm	8g	2mm.
139	I4/mmm	8f	..2/m
139	I4/mmm	4e	4mm
139	I4/mmm	4d	-4m2
139	I4/mmm	4c	mmm.
139	I4/mmm	2b	4/mmm
139	I4/mmm	2a	4/mmm
140	I4/mcm	32m	1
140	I4/mcm	16l	..m
140	I4/mcm	16k	m..
140	I4/mcm	16j	.2.
140	I4/mcm	16i	..2
140	I4/mcm	8h	m.2m
140	I4/mcm	8g	2.mm
140	I4/mcm	8f	4..
140	I4/mcm	8e	..2/m
140	I4/mcm	4d	m.mm
140	I4/mcm	4c	4/m..
140	I4/mcm	4b	-42m
140	I4/mcm	4a	422
141	I41/amd	32i	1
141	I41/amd	16h	.m.
141	I41/amd	16g	..2
141	I41/amd	16f	.2.
141	I41/amd	8e	2mm.
141	I41/amd	8d	.2/m.
141	I41/amd	8c	.2/m.
141	I41/amd	4b	-4m2
141	I41/amd	4a	-4m2
142	I41/acd	32g	1
142	I41/acd	16f	..2
142	I41/acd	16e	.2.
142	I41/acd	16d	2..
142	I41/acd	16c	-1
142	I41/acd	8b	2.22
142	I41/acd	8a	-4..
143	P3	3d	1
143	P3	1c	3..
143	P3	1b	3..
143	P3	1a	3..
144	P31	3a	1
145	P32	3a	1
146	R3	9b	1
146	R3	3a	3.
147	P-3	6g	1
147	P-3	3f	-1
147	P-3	3e	-1
147	P-3	2d	3..
147	P-3	2c	3..
147	P-3	1b	-3..
147	P-3	1a	-3..
148	R-3	18f	1
148	R-3	9e	-1
148	R-3	9d	-1
148	R-3	6c	3.
148	R-3	3b	-3.
148	R-3	3a	-3.
149	P312	6l	1
149	P312	3k	..2
149	P312	3j	..2
149	P312	2i	3..
149	P312	2h	3..
149	P312	2g	3..
149	P312	1f	3.2
149	P312	1e	3.2
149	P312	1d	3.2
149	P312	1c	3.2
149	P312	1b	3.2
149	P312	1a	3.2
150	P321	6g	1
150	P321	3f	.2.
150	P321	3e	.2.
150	P321	2d	3..
150	P321	2c	3..
150	P321	1b	32.
150	P321	1a	32.
151	P3112	6c	1
151	P3112	3b	..2
151	P3112	3a	..2
152	P3121	6c	1
152	P3121	3b	.2.
152	P3121	3a	.2.
153	P3212	6c	1
153	P3212	3b	..2
153	P3212	3a	..2
154	P3221	6c	1
154	P3221	3b	.2.
154	P3221	3a	.2.
155	R32	18f	1
155	R32	9e	.2
155	R32	9d	.2
155	R32	6c	3.
155	R32	3b	32
155	R32	3a	32
156	P3m1	6e	1
156	P3m1	3d	.m.
156	P3m1	1c	3m.
156	P3m1	1b	3m.
156	P3m1	1a	3m.
157	P31m	6d	1
157	P31m	3c	..m
157	P31m	2b	3..
157	P31m	1a	3.m
158	P3c1	6d	1
158	P3c1	2c	3..
158	P3c1	2b	3..
158	P3c1	2a	3..
159	P31c	6c	1
159	P31c	2b	3..
159	P31c	2a	3..
160	R3m	18c	1
160	R3m	9b	.m
160	R3m	3a	3m
161	R3c	18b	1
161	R3c	6a	3.
162	P-31m	12l	1
162	P-31m	6k	..m
162	P-31m	6j	..2
162	P-31m	6i	..2
162	P-31m	4h	3..
162	P-31m	3g	..2/m
162	P-31m	3f	..2/m
162	P-31m	2e	3.m
162	P-31m	2d	3.2
162	P-31m	2c	3.2
162	P-31m	1b	-3.m
162	P-31m	1a	-3.m
163	P-31c	12i	1
163	P-31c	6h	..2
163	P-31c	6g	-1
163	P-31c	4f	3..
163	P-31c	4e	3..
163	P-31c	2d	3.2
163	P-31c	2c	3.2
163	P-31c	2b	-3..
163	P-31c	2a	3.2
164	P-3m1	12j	1
164	P-3m1	6i	.m.
164	P-3m1	6h	.2.
164	P-3m1	6g	.2.
164	P-3m1	3f	.2/m.
164	P-3m1	3e	.2/m.
164	P-3m1	2d	3m.
164	P-3m1	2c	3m.
164	P-3m1	1b	-3m.
164	P-3m1	1a	-3m.
165	P-3c1	12g	1
165	P-3c1	6f	.2.
165	P-3c1	6e	-1
165	P-3c1	4d	3..
165	P-3c1	4c	3..
165	P-3c1	2b	-3..
165	P-3c1	2a	32.
166	R-3m	36i	1
166	R-3m	18h	.m
166	R-3m	18g	.2
166	R-3m	18f	.2
166	R-3m	9e	.2/m
166	R-3m	9d	.2/m
166	R-3m	6c	3m
166	R-3m	3b	-3m
166	R-3m	3a	-3m
167	R-3c	36f	1
167	R-3c	18e	.2
167	R-3c	18d	-1
167	R-3c	12c	3.
167	R-3c	6b	-3.
167	R-3c	6a	32
168	P6	6d	1
168	P6	3c	2..
168	P6	2b	3..
168	P6	1a	6..
169	P61	6a	1
170	P65	6a	1
171	P62	6c	1
171	P62	3b	2..
171	P62	3a	2..
172	P64	6c	1
172	P64	3b	2..
172	P64	3a	2..
173	P63	6c	1
173	P63	2b	3..
173	P63	2a	3..
174	P-6	6l	1
174	P-6	3k	m..
174	P-6	3j	m..
174	P-6	2i	3..
174	P-6	2h	3..
174	P-6	2g	3..
174	P-6	1f	-6..
174	P-6	1e	-6..
174	P-6	1d	-6..
174	P-6	1c	-6..
174	P-6	1b	-6..
174	P-6	1a	-6..
175	P6/m	12l	1
175	P6/m	6k	m..
175	P6/m	6j	m..
175	P6/m	6i	2..
175	P6/m	4h	3..
175	P6/m	3g	2/m..
175	P6/m	3f	2/m..
175	P6/m	2e	6..
175	P6/m	2d	-6..
175	P6/m	2c	-6..
175	P6/m	1b	6/m..
175	P6/m	1a	6/m..
176	P63/m	12i	1
176	P63/m	6h	m..
176	P63/m	6g	-1
176	P63/m	4f	3..
176	P63/m	4e	3..
176	P63/m	2d	-6..
176	P63/m	2c	-6..
176	P63/m	2b	-3..
176	P63/m	2a	-6..
177	P622	12n	1
177	P622	6m	..2
177	P622	6l	..2
177	P622	6k	.2.
177	P622	6j	.2.
177	P622	6i	2..
177	P622	4h	3..
177	P622	3g	222
177	P622	3f	222
177	P622	2e	6..
177	P622	2d	3.2
177	P622	2c	3.2
177	P622	1b	622
177	P622	1a	622
178	P6122	12c	1
178	P6122	6b	..2
178	P6122	6a	.2.
179	P6522	12c	1
179	P6522	6b	..2
179	P6522	6a	.2.
180	P6222	12k	1
180	P6222	6j	..2
180	P6222	6i	..2
180	P6222	6h	.2.
180	P6222	6g	.2.
180	P6222	6f	2..
180	P6222	6e	2..
180	P6222	3d	222
180	P6222	3c	222
180	P6222	3b	222
180	P6222	3a	222
181	P6422	12k	1
181	P6422	6j	..2
181	P6422	6i	..2
181	P6422	6h	.2.
181	P6422	6g	.2.
181	P6422	6f	2..
181	P6422	6e	2..
181	P6422	3d	222
181	P6422	3c	222
181	P6422	3b	222
181	P6422	3a	222
182	P6322	12i	1
182	P6322	6h	..2
182	P6322	6g	.2.
182	P6322	4f	3..
182	P6322	4e	3..
182	P6322	2d	3.2
182	P6322	2c	3.2
182	P6322	2b	3.2
182	P6322	2a	32.
183	P6mm	12f	1
183	P6mm	6e	.m.
183	P6mm	6d	..m
183	P6mm	3c	2mm
183	P6mm	2b	3m.
183	P6mm	1a	6mm
184	P6cc	12d	1
184	P6cc	6c	2..
184	P6cc	4b	3..
184	P6cc	2a	6..
185	P63cm	12d	1
185	P63cm	6c	..m
185	P63cm	4b	3..
185	P63cm	2a	3.m
186	P63mc	12d	1
186	P63mc	6c	.m.
186	P63mc	2b	3m.
186	P63mc	2a	3m.
187	P-6m2	12o	1
187	P-6m2	6n	.m.
187	P-6m2	6m	m..
187	P-6m2	6l	m..
187	P-6m2	3k	mm2
187	P-6m2	3j	mm2
187	P-6m2	2i	3m.
187	P-6m2	2h	3m.
187	P-6m2	2g	3m.
187	P-6m2	1f	-6m2
187	P-6m2	1e	-6m2
187	P-6m2	1d	-6m2
187	P-6m2	1c	-6m2
187	P-6m2	1b	-6m2
187	P-6m2	1a	-6m2
188	P-6c2	12l	1
188	P-6c2	6k	m..
188	P-6c2	6j	..2
188	P-6c2	4i	3..
188	P-6c2	4h	3..
188	P-6c2	4g	3..
188	P-6c2	2f	-6..
188	P-6c2	2e	3.2
188	P-6c2	2d	-6..
188	P-6c2	2c	3.2
188	P-6c2	2b	-6..
188	P-6c2	2a	3.2
189	P-62m	12l	1
189	P-62m	6k	m..
189	P-62m	6j	m..
189	P-62m	6i	..m
189	P-62m	4h	3..
189	P-62m	3g	m2m
189	P-62m	3f	m2m
189	P-62m	2e	3.m
189	P-62m	2d	-6..
189	P-62m	2c	-6..
189	P-62m	1b	-62m
189	P-62m	1a	-62m
190	P-62c	12i	1
190	P-62c	6h	m..
190	P-62c	6g	.2.
190	P-62c	4f	3..
190	P-62c	4e	3..
190	P-62c	2d	-6..
190	P-62c	2c	-6..
190	P-62c	2b	-6..
190	P-62c	2a	32.
191	P6/mmm	24r	1
191	P6/mmm	12q	m..
191	P6/mmm	12p	m..
191	P6/mmm	12o	.m.
191	P6/mmm	12n	..m
191	P6/mmm	6m	mm2
191	P6/mmm	6l	mm2
191	P6/mmm	6k	m2m
191	P6/mmm	6j	m2m
191	P6/mmm	6i	2mm
191	P6/mmm	4h	3m.
191	P6/mmm	3g	mmm
191	P6/mmm	3f	mmm
191	P6/mmm	2e	6mm
191	P6/mmm	2d	-6m2
191	P6/mmm	2c	-6m2
191	P6/mmm	1b	6/mmm
191	P6/mmm	1a	6/mmm
192	P6/mcc	24m	1
192	P6/mcc	12l	m..
192	P6/mcc	12k	..2
192	P6/mcc	12j	.2.
192	P6/mcc	12i	2..
192	P6/mcc	8h	3..
192	P6/mcc	6g	2/m..
192	P6/mcc	6f	222
192	P6/mcc	4e	6..
192	P6/mcc	4d	-6..
192	P6/mcc	4c	3.2
192	P6/mcc	2b	6/m..
192	P6/mcc	2a	622
193	P63/mcm	24l	1
193	P63/mcm	12k	..m
193	P63/mcm	12j	m..
193	P63/mcm	12i	..2
193	P63/mcm	8h	3..
193	P63/mcm	6g	m2m
193	P63/mcm	6f	..2/m
193	P63/mcm	4e	3.m
193	P63/mcm	4d	3.2
193	P63/mcm	4c	-6..
193	P63/mcm	2b	-3.m
193	P63/mcm	2a	-62m
194	P63/mmc	24l	1
194	P63/mmc	12k	.m.
194	P63/mmc	12j	m..
194	P63/mmc	12i	.2.
194	P63/mmc	6h	mm2
194	P63/mmc	6g	.2/m.
194	P63/mmc	4f	3m.
194	P63/mmc	4e	3m.
194	P63/mmc	2d	-6m2
194	P63/mmc	2c	-6m2
194	P63/mmc	2b	-6m2
194	P63/mmc	2a	-3m.
195	P23	12j	1
195	P23	6i	2..
195	P23	6h	2..
195	P23	6g	2..
195	P23	6f	2..
195	P23	4e	.3.
195	P23	3d	222..
195	P23	3c	222..
195	P23	1b	23.
195	P23	1a	23.
196	F23	48h	1
196	F23	24g	2..
196	F23	24f	2..
196	F23	16e	.3.
196	F23	4d	23.
196	F23	4c	23.
196	F23	4b	23.
196	F23	4a	23.
197	I23	24f	1
197	I23	12e	2..
197	I23	12d	2..
197	I23	8c	.3.
197	I23	6b	222..
197	I23	2a	23.
198	P213	12b	1
198	P213	4a	.3.
199	I213	24c	1
199	I213	12b	2..
199	I213	8a	.3.
200	Pm-3	24l	1
200	Pm-3	12k	m..
200	Pm-3	12j	m..
200	Pm-3	8i	.3.
200	Pm-3	6h	mm2..
200	Pm-3	6g	mm2..
200	Pm-3	6f	mm2..
200	Pm-3	6e	mm2..
200	Pm-3	3d	mmm..
200	Pm-3	3c	mmm..
200	Pm-3	1b	m-3.
200	Pm-3	1a	m-3.
201	Pn-3	24h	1
201	Pn-3	12g	2..
201	Pn-3	12f	2..
201	Pn-3	8e	.3.
201	Pn-3	6d	222..
201	Pn-3	4c	.-3.
201	Pn-3	4b	.-3.
201	Pn-3	2a	23.
202	Fm-3	96i	1
202	Fm-3	48h	m..
202	Fm-3	48g	2..
202	Fm-3	32f	.3.
202	Fm-3	24e	mm2..
202	Fm-3	24d	2/m..
202	Fm-3	8c	23.
202	Fm-3	4b	m-3.
202	Fm-3	4a	m-3.
203	Fd-3	96g	1
203	Fd-3	48f	2..
203	Fd-3	32e	.3.
203	Fd-3	16d	.-3.
203	Fd-3	16c	.-3.
203	Fd-3	8b	23.
203	Fd-3	8a	23.
204	Im-3	48h	1
204	Im-3	24g	m..
204	Im-3	16f	.3.
204	Im-3	12e	mm2..
204	Im-3	12d	mm2..
204	Im-3	8c	.-3.
204	Im-3	6b	mmm..
204	Im-3	2a	m-3.
205	Pa-3	24d	1
205	Pa-3	8c	.3.
205	Pa-3	4b	.-3.
205	Pa-3	4a	.-3.
206	Ia-3	48e	1
206	Ia-3	24d	2..
206	Ia-3	16c	.3.
206	Ia-3	8b	.-3.
206	Ia-3	8a	.-3.
207	P432	24k	1
207	P432	12j	..2
207	P432	12i	..2
207	P432	12h	2..
207	P432	8g	.3.
207	P432	6f	4..
207	P432	6e	4..
207	P432	3d	42.2
207	P432	3c	42.2
207	P432	1b	432
207	P432	1a	432
208	P4232	24m	1
208	P4232	12l	..2
208	P4232	12k	..2
208	P4232	12j	2..
208	P4232	12i	2..
208	P4232	12h	2..
208	P4232	8g	.3.
208	P4232	6f	2.22
208	P4232	6e	2.22
208	P4232	6d	222..
208	P4232	4c	.32
208	P4232	4b	.32
208	P4232	2a	23.
209	F432	96j	1
209	F432	48i	2..
209	F432	48h	..2
209	F432	48g	..2
209	F432	32f	.3.
209	F432	24e	4..
209	F432	24d	2.22
209	F432	8c	23.
209	F432	4b	432
209	F432	4a	432
210	F4132	96h	1
210	F4132	48g	..2
210	F4132	48f	2..
210	F4132	32e	.3.
210	F4132	16d	.32
210	F4132	16c	.32
210	F4132	8b	23.
210	F4132	8a	23.
211	I432	48j	1
211	I432	24i	..2
211	I432	24h	..2
211	I432	24g	2..
211	I432	16f	.3.
211	I432	12e	4..
211	I432	12d	2.22
211	I432	8c	.32
211	I432	6b	42.2
211	I432	2a	432
212	P4332	24e	1
212	P4332	12d	..2
212	P4332	8c	.3.
212	P4332	4b	.32
212	P4332	4a	.32
213	P4132	24e	1
213	P4132	12d	..2
213	P4132	8c	.3.
213	P4132	4b	.32
213	P4132	4a	.32
214	I4132	48i	1
214	I4132	24h	..2
214	I4132	24g	..2
214	I4132	24f	2..
214	I4132	16e	.3.
214	I4132	12d	2.22
214	I4132	12c	2.22
214	I4132	8b	.32
214	I4132	8a	.32
215	P-43m	24j	1
215	P-43m	12i	..m
215	P-43m	12h	2..
215	P-43m	6g	2.mm
215	P-43m	6f	2.mm
215	P-43m	4e	.3m
215	P-43m	3d	-42.m
215	P-43m	3c	-42.m
215	P-43m	1b	-43m
215	P-43m	1a	-43m
216	F-43m	96i	1
216	F-43m	48h	..m
216	F-43m	24g	2.mm
216	F-43m	24f	2.mm
216	F-43m	16e	.3m
216	F-43m	4d	-43m
216	F-43m	4c	-43m
216	F-43m	4b	-43m
216	F-43m	4a	-43m
217	I-43m	48h	1
217	I-43m	24g	..m
217	I-43m	24f	2..
217	I-43m	12e	2.mm
217	I-43m	12d	-4..
217	I-43m	8c	.3m
217	I-43m	6b	-42.m
217	I-43m	2a	-43m
218	P-43n	24i	1
218	P-43n	12h	2..
218	P-43n	12g	2..
218	P-43n	12f	2..
218	P-43n	8e	.3.
218	P-43n	6d	-4..
218	P-43n	6c	-4..
218	P-43n	6b	222..
218	P-43n	2a	23.
219	F-43c	96h	1
219	F-43c	48g	2..
219	F-43c	48f	2..
219	F-43c	32e	.3.
219	F-43c	24d	-4..
219	F-43c	24c	-4..
219	F-43c	8b	23.
219	F-43c	8a	23.
220	I-43d	48e	1
220	I-43d	24d	2..
220	I-43d	16c	.3.
220	I-43d	12b	-4..
220	I-43d	12a	-4..
221	Pm-3m	48n	1
221	Pm-3m	24m	..m
221	Pm-3m	24l	m..
221	Pm-3m	24k	m..
221	Pm-3m	12j	m.m2
221	Pm-3m	12i	m.m2
221	Pm-3m	12h	mm2..
221	Pm-3m	8g	.3m
221	Pm-3m	6f	4m.m
221	Pm-3m	6e	4m.m
221	Pm-3m	3d	4/mm.m
221	Pm-3m	3c	4/mm.m
221	Pm-3m	1b	m-3m
221	Pm-3m	1a	m-3m
222	Pn-3n	48i	1
222	Pn-3n	24h	..2
222	Pn-3n	24g	2..
222	Pn-3n	16f	.3.
222	Pn-3n	12e	4..
222	Pn-3n	12d	-4..
222	Pn-3n	8c	.-3.
222	Pn-3n	6b	42.2
222	Pn-3n	2a	432
223	Pm-3n	48l	1
223	Pm-3n	24k	m..
223	Pm-3n	24j	..2
223	Pm-3n	16i	.3.
223	Pm-3n	12h	mm2..
223	Pm-3n	12g	mm2..
223	Pm-3n	12f	mm2..
223	Pm-3n	8e	.32
223	Pm-3n	6d	-4m.2
223	Pm-3n	6c	-4m.2
223	Pm-3n	6b	mmm..
223	Pm-3n	2a	m-3.
224	Pn-3m	48l	1
224	Pn-3m	24k	..m
224	Pn-3m	24j	..2
224	Pn-3m	24i	..2
224	Pn-3m	24h	2..
224	Pn-3m	12g	2.mm
224	Pn-3m	12f	2.22
224	Pn-3m	8e	.3m
224	Pn-3m	6d	-42.m
224	Pn-3m	4c	.-3m
224	Pn-3m	4b	.-3m
224	Pn-3m	2a	-43m
225	Fm-3m	192l	1
225	Fm-3m	96k	..m
225	Fm-3m	96j	m..
225	Fm-3m	48i	m.m2
225	Fm-3m	48h	m.m2
225	Fm-3m	48g	2.mm
225	Fm-3m	32f	.3m
225	Fm-3m	24e	4m.m
225	Fm-3m	24d	m.mm
225	Fm-3m	8c	-43m
225	Fm-3m	4b	m-3m
225	Fm-3m	4a	m-3m
226	Fm-3c	192j	1
226	Fm-3c	96i	m..
226	Fm-3c	96h	..2
226	Fm-3c	64g	.3.
226	Fm-3c	48f	4..
226	Fm-3c	48e	mm2..
226	Fm-3c	24d	4/m..
226	Fm-3c	24c	-4m.2
226	Fm-3c	8b	m-3.
226	Fm-3c	8a	432
227	Fd-3m	192i	1
227	Fd-3m	96h	..2
227	Fd-3m	96g	..m
227	Fd-3m	48f	2.mm
227	Fd-3m	32e	.3m
227	Fd-3m	16d	.-3m
227	Fd-3m	16c	.-3m
227	Fd-3m	8b	-43m
227	Fd-3m	8a	-43m
228	Fd-3c	192h	1
228	Fd-3c	96g	..2
228	Fd-3c	96f	2..
228	Fd-3c	64e	.3.
228	Fd-3c	48d	-4..
228	Fd-3c	32c	.-3.
228	Fd-3c	32b	.32
228	Fd-3c	16a	23.
229	Im-3m	96l	1
229	Im-3m	48k	..m
229	Im-3m	48j	m..
229	Im-3m	48i	..2
229	Im-3m	24h	m.m2
229	Im-3m	24g	mm2..
229	Im-3m	16f	.3m
229	Im-3m	12e	4m.m
229	Im-3m	12d	-4m.2
229	Im-3m	8c	.-3m
229	Im-3m	6b	4/mm.m
229	Im-3m	2a	m-3m
230	Ia-3d	96h	1
230	Ia-3d	48g	..2
230	Ia-3d	48f	2..
230	Ia-3d	32e	.3.
230	Ia-3d	24d	-4..
230	Ia-3d	24c	2.22
230	Ia-3d	16b	.32
230	Ia-3d	16a	.-3.

References

For the use of this function, please cite the following paper.

@inproceedings{levy2024symmcd,
title={Symm{CD}: Symmetry-Preserving Crystal Generation with Diffusion Models},
author={Daniel Levy and Siba Smarak Panigrahi and S{\'e}kou-Oumar Kaba and Qiang Zhu and Mikhail Galkin and Santiago Miret and Siamak Ravanbakhsh},
booktitle={AI for Accelerated Materials Design - NeurIPS 2024},
year={2024},
url={https://openreview.net/forum?id=V7x2KZQn2v}
}