[docs]
ELEMENT_NAMES = {
1: "H",
2: "He",
3: "Li",
4: "Be",
5: "B",
6: "C",
7: "N",
8: "O",
9: "F",
10: "Ne",
11: "Na",
12: "Mg",
13: "Al",
14: "Si",
15: "P",
16: "S",
17: "Cl",
18: "Ar",
19: "K",
20: "Ca",
21: "Sc",
22: "Ti",
23: "V",
24: "Cr",
25: "Mn",
26: "Fe",
27: "Co",
28: "Ni",
29: "Cu",
30: "Zn",
31: "Ga",
32: "Ge",
33: "As",
34: "Se",
35: "Br",
36: "Kr",
37: "Rb",
38: "Sr",
39: "Y",
40: "Zr",
41: "Nb",
42: "Mo",
43: "Tc",
44: "Ru",
45: "Rh",
46: "Pd",
47: "Ag",
48: "Cd",
49: "In",
50: "Sn",
51: "Sb",
52: "Te",
53: "I",
54: "Xe",
55: "Cs",
56: "Ba",
57: "La",
58: "Ce",
59: "Pr",
60: "Nd",
61: "Pm",
62: "Sm",
63: "Eu",
64: "Gd",
65: "Tb",
66: "Dy",
67: "Ho",
68: "Er",
69: "Tm",
70: "Yb",
71: "Lu",
72: "Hf",
73: "Ta",
74: "W",
75: "Re",
76: "Os",
77: "Ir",
78: "Pt",
79: "Au",
80: "Hg",
81: "Tl",
82: "Pb",
83: "Bi",
84: "Po",
85: "At",
86: "Rn",
87: "Fr",
88: "Ra",
89: "Ac",
90: "Th",
91: "Pa",
92: "U",
93: "Np",
94: "Pu",
95: "Am",
96: "Cm",
97: "Bk",
98: "Cf",
99: "Es",
100: "Fm",
101: "Md",
102: "No",
103: "Lr",
104: "Rf",
105: "Db",
106: "Sg",
107: "Bh",
108: "Hs",
109: "Mt",
110: "Ds",
111: "Rg",
112: "Cn",
113: "Nh",
114: "Fl",
115: "Mc",
116: "Lv",
117: "Ts",
118: "Og",
}
[docs]
ATOMIC_MASS = {
1: 1.00794,
2: 4.002602,
3: 6.941,
4: 9.012182,
5: 10.811,
6: 12.0107,
7: 14.0067,
8: 15.9994,
9: 18.9984032,
10: 20.1797,
11: 22.98976928,
12: 24.305,
13: 26.9815386,
14: 28.0855,
15: 30.973762,
16: 32.065,
17: 35.453,
18: 39.948,
19: 39.0983,
20: 40.078,
21: 44.955912,
22: 47.867,
23: 50.9415,
24: 51.9961,
25: 54.938045,
26: 55.845,
27: 58.933195,
28: 58.6934,
29: 63.546,
30: 65.409,
31: 69.723,
32: 72.64,
33: 74.9216,
34: 78.96,
35: 79.904,
36: 83.798,
37: 85.4678,
38: 87.62,
39: 88.90585,
40: 91.224,
41: 92.90638,
42: 95.94,
43: 98.0,
44: 101.07,
45: 102.9055,
46: 106.42,
47: 107.8682,
48: 112.411,
49: 114.818,
50: 118.71,
51: 121.76,
52: 127.6,
53: 126.90447,
54: 131.293,
55: 132.9054519,
56: 137.327,
57: 138.90547,
58: 140.116,
59: 140.90765,
60: 144.242,
61: 145.0,
62: 150.36,
63: 151.964,
64: 157.25,
65: 158.92535,
66: 162.5,
67: 164.93032,
68: 167.259,
69: 168.93421,
70: 173.04,
71: 174.967,
72: 178.49,
73: 180.94788,
74: 183.84,
75: 186.207,
76: 190.23,
77: 192.217,
78: 195.084,
79: 196.966569,
80: 200.59,
81: 204.3833,
82: 207.2,
83: 208.9804,
84: 210.0,
85: 210.0,
86: 220.0,
87: 223.0,
88: 226.0,
89: 227.0,
90: 232.03806,
91: 231.03588,
92: 238.02891,
93: 237.0,
94: 244.0,
95: 243.0,
96: 247.0,
97: 247.0,
98: 251.0,
99: 252.0,
100: 257.0,
101: 258.0,
102: 259.0,
103: 262.0,
104: 267.0,
105: 268.0,
106: 269.0,
107: 270.0,
108: 270.0,
109: 278.0,
110: 281.0,
111: 282.0,
112: 285.0,
113: 286.0,
114: 289.0,
115: 290.0,
116: 293.0,
117: 294.0,
118: 294.0,
}
[docs]
OXIDATION_STATES = {
1: [-1, 1],
2: [0],
3: [0, 1],
4: [0, 1, 2],
5: [-5, -1, 0, 1, 2, 3],
6: [-4, -3, -2, -1, 0, 1, 2, 3, 4],
7: [-3, -2, -1, 0, 1, 2, 3, 4, 5],
8: [-2, -1, 0, 1, 2],
9: [-1, 0],
10: [0],
11: [-1, 0, 1],
12: [0, 1, 2],
13: [-2, -1, 0, 1, 2, 3],
14: [-4, -3, -2, -1, 0, 1, 2, 3, 4],
15: [-3, -2, -1, 0, 1, 2, 3, 4, 5],
16: [-2, -1, 0, 1, 2, 3, 4, 5, 6],
17: [-1, 1, 2, 3, 4, 5, 6, 7],
18: [0],
19: [-1, 1],
20: [1, 2],
21: [0, 1, 2, 3],
22: [-2, -1, 0, 1, 2, 3, 4],
23: [-3, -1, 0, 1, 2, 3, 4, 5],
24: [-4, -2, -1, 0, 1, 2, 3, 4, 5, 6],
25: [-3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7],
26: [-4, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7],
27: [-3, -1, 0, 1, 2, 3, 4, 5],
28: [-2, -1, 0, 1, 2, 3, 4],
29: [-2, 0, 1, 2, 3, 4],
30: [-2, 0, 1, 2],
31: [-5, -4, -3, -2, -1, 0, 1, 2, 3],
32: [-4, -3, -2, -1, 0, 1, 2, 3, 4],
33: [-3, -2, -1, 0, 1, 2, 3, 4, 5],
34: [-2, -1, 0, 1, 2, 3, 4, 5, 6],
35: [-1, 1, 2, 3, 4, 5, 7],
36: [0, 1, 2],
37: [-1, 1],
38: [1, 2],
39: [0, 1, 2, 3],
40: [-2, 0, 1, 2, 3, 4],
41: [-3, -1, 0, 1, 2, 3, 4, 5],
42: [-4, -2, -1, 0, 1, 2, 3, 4, 5, 6],
43: [-3, -1, 0, 1, 2, 3, 4, 5, 6, 7],
44: [-4, -2, 0, 1, 2, 3, 4, 5, 6, 7, 8],
45: [-3, -1, 0, 1, 2, 3, 4, 5, 6, 7],
46: [0, 1, 2, 3, 4, 5],
47: [-2, -1, 0, 1, 2, 3],
48: [-2, 1, 2],
49: [-5, -2, -1, 0, 1, 2, 3],
50: [-4, -3, -2, -1, 0, 1, 2, 3, 4],
51: [-3, -2, -1, 0, 1, 2, 3, 4, 5],
52: [-2, -1, 0, 1, 2, 3, 4, 5, 6],
53: [-1, 1, 2, 3, 4, 5, 6, 7],
54: [0, 2, 4, 6, 8],
55: [-1, 1],
56: [1, 2],
57: [0, 1, 2, 3],
58: [2, 3, 4],
59: [0, 1, 2, 3, 4, 5],
60: [0, 2, 3, 4],
61: [2, 3],
62: [0, 1, 2, 3],
63: [0, 2, 3],
64: [0, 1, 2, 3],
65: [0, 1, 2, 3, 4],
66: [0, 2, 3, 4],
67: [0, 2, 3],
68: [0, 2, 3],
69: [0, 1, 2, 3],
70: [0, 1, 2, 3],
71: [0, 2, 3],
72: [-2, 0, 1, 2, 3, 4],
73: [-3, -1, 0, 1, 2, 3, 4, 5],
74: [-4, -2, -1, 0, 1, 2, 3, 4, 5, 6],
75: [-3, -1, 0, 1, 2, 3, 4, 5, 6, 7],
76: [-4, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8],
77: [-3, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
78: [-3, -2, -1, 0, 1, 2, 3, 4, 5, 6],
79: [-3, -2, -1, 0, 1, 2, 3, 5],
80: [-2, 1, 2],
81: [-5, -2, -1, 1, 2, 3],
82: [-4, -2, -1, 0, 1, 2, 3, 4],
83: [-3, -2, -1, 0, 1, 2, 3, 4, 5],
84: [-2, 2, 4, 5, 6],
85: [-1, 1, 3, 5, 7],
86: [2, 6],
87: [1],
88: [2],
89: [2, 3],
90: [-1, 1, 2, 3, 4],
91: [2, 3, 4, 5],
92: [-1, 1, 2, 3, 4, 5, 6],
93: [2, 3, 4, 5, 6, 7],
94: [2, 3, 4, 5, 6, 7, 8],
95: [2, 3, 4, 5, 6, 7],
96: [3, 4, 5, 6],
97: [2, 3, 4, 5],
98: [2, 3, 4, 5],
99: [2, 3, 4],
100: [2, 3],
101: [2, 3],
102: [2, 3],
103: [3],
104: [4],
105: [5],
106: [0, 6],
107: [7],
108: [8],
109: [0],
110: [0],
111: [0],
112: [2],
113: [0],
114: [0],
115: [0],
116: [0],
117: [0],
118: [0],
}
[docs]
HEXAGONAL = "hexagonal"
[docs]
MONOCLINIC = "monoclinic"
[docs]
ORTHORHOMBIC = "orthorhombic"
[docs]
RHOMBOHEDRAL = "rhombohedral"
[docs]
TETRAGONAL = "tetragonal"
[docs]
TRICLINIC = "triclinic"
[docs]
LATTICE_SYSTEMS = [
CUBIC,
HEXAGONAL,
MONOCLINIC,
ORTHORHOMBIC,
RHOMBOHEDRAL,
TETRAGONAL,
TRICLINIC,
]
# See: https://en.wikipedia.org/wiki/Crystal_system#Crystal_classes
# Each item in the dictionary contains a list of:
# - crystal system name
# - crystal class indices in the crystal system
# - point symmetry indices in the crystal system
[docs]
CRYSTAL_SYSTEMS = {
1: ["triclinic", [1, 2], [1, 2]],
2: ["monoclinic", [3, 4, 5], [1, 3, 2]],
3: ["orthorhombic", [6, 7, 8], [4, 3, 2]],
4: ["tetragonal", [9, 10, 11, 12, 13, 14, 15], [1, 5, 2, 4, 3]],
5: ["trigonal", [16, 17, 18, 19, 20], [1, 2, 4, 3]],
6: ["hexagonal", [21, 22, 23, 24, 25, 26, 27], [1, 5, 2, 4, 3]],
7: ["cubic", [28, 29, 30, 31, 32], [4, 2, 5]],
}
[docs]
CRYSTAL_SYSTEMS_MINIMAL = {
1: "triclinic",
2: "monoclinic",
3: "orthorhombic",
4: "tetragonal",
5: "trigonal",
6: "hexagonal",
7: "cubic",
}
# See: https://en.wikipedia.org/wiki/Crystal_system#Crystal_classes
# See: http://pd.chem.ucl.ac.uk/pdnn/symm2/group32.htm
# Each item in the dictionary contains a list of:
# - crystal class name
# - crystal system
# - list of point groups as in pymatgen
# - point symmetry
# - space groups
[docs]
CRYSTAL_CLASSES = {
1: ["pedial", "triclinic", ["1"], "enantiomorphic-polar", [1]],
2: ["pinacoidal", "triclinic", ["-1"], "centrosymmetric", [2]],
3: ["sphenoidal", "monoclinic", ["2"], "enantiomorphic-polar", [3, 4, 5]],
4: ["domatic", "monoclinic", ["m"], "polar", [6, 7, 8, 9]],
5: [
"prismatic",
"monoclinic",
["2/m"],
"centrosymmetric",
[10, 11, 12, 13, 14, 15],
],
6: [
"rhombic-disphenoidal",
"orthorhombic",
["222"],
"enantiomorphic",
[16, 17, 18, 19, 20, 21, 22, 23, 24],
],
7: [
"rhombic-pyramidal",
"orthorhombic",
["mm2"],
"polar",
[
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38,
39,
40,
41,
42,
43,
44,
45,
46,
],
],
8: [
"rhombic-dipyramidal",
"orthorhombic",
["mmm"],
"centrosymmetric",
[
47,
48,
49,
50,
51,
52,
53,
54,
55,
56,
57,
58,
59,
60,
61,
62,
63,
64,
65,
66,
67,
68,
69,
70,
71,
72,
73,
74,
],
],
9: [
"tetragonal-pyramidal",
"tetragonal",
["4"],
"enantiomorphic-polar",
[75, 76, 77, 78, 79, 80],
],
10: [
"tetragonal-disphenoidal",
"tetragonal",
["-4"],
"non-centrosymmetric",
[81, 82],
],
11: [
"tetragonal-dipyramidal",
"tetragonal",
["4/m"],
"centrosymmetric",
[83, 84, 85, 86, 87, 88],
],
12: [
"tetragonal-trapezohedral",
"tetragonal",
["422"],
"enantiomorphic",
[89, 90, 91, 92, 93, 94, 95, 96, 97, 98],
],
13: [
"ditetragonal-pyramidal",
"tetragonal",
["4mm"],
"polar",
[99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110],
],
14: [
"tetragonal-scalenohedral",
"tetragonal",
["-42m", "-4m2"],
"non-centrosymmetric",
[111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122],
],
15: [
"ditetragonal-dipyramidal",
"tetragonal",
["4/mmm"],
"centrosymmetric",
[
123,
124,
125,
126,
127,
128,
129,
130,
131,
132,
133,
134,
135,
136,
137,
138,
139,
140,
141,
142,
],
],
16: [
"trigonal-pyramidal",
"trigonal",
["3"],
"enantiomorphic-polar",
[143, 144, 145, 146],
],
17: ["rhombohedral", "trigonal", ["-3"], "centrosymmetric", [147, 148]],
18: [
"trigonal-trapezohedral",
"trigonal",
["32", "321", "312"],
"enantiomorphic",
[149, 150, 151, 152, 153, 154, 155],
],
19: [
"ditrigonal-pyramidal",
"trigonal",
["3m", "3m1", "31m"],
"polar",
[156, 157, 158, 159, 160, 161],
],
20: [
"ditrigonal-scalenohedral",
"trigonal",
["-3m", "-3m1", "-31m"],
"centrosymmetric",
[162, 163, 164, 165, 166, 167],
],
21: [
"hexagonal-pyramidal",
"hexagonal",
["6"],
"enantiomorphic-polar",
[168, 169, 170, 171, 172, 173],
],
22: ["trigonal-dipyramidal", "hexagonal", ["-6"], "non-centrosymmetric", [174]],
23: [
"hexagonal-dipyramidal",
"hexagonal",
["6/m"],
"centrosymmetric",
[175, 176],
],
24: [
"hexagonal-trapezohedral",
"hexagonal",
["622"],
"enantiomorphic",
[177, 178, 179, 180, 181, 182],
],
25: [
"dihexagonal-pyramidal",
"hexagonal",
["6mm"],
"polar",
[183, 184, 185, 186],
],
26: [
"ditrigonal-dipyramidal",
"hexagonal",
["-6m2", "-62m"],
"non-centrosymmetric",
[187, 188, 189, 190],
],
27: [
"dihexagonal-dipyramidal",
"hexagonal",
["6/mmm"],
"centrosymmetric",
[191, 192, 193, 194],
],
28: ["tetartoidal", "cubic", ["23"], "enantiomorphic", [195, 196, 197, 198, 199]],
29: [
"diploidal",
"cubic",
["m-3"],
"centrosymmetric",
[200, 201, 202, 203, 204, 205, 206],
],
30: [
"gyroidal",
"cubic",
["432"],
"enantiomorphic",
[207, 208, 209, 210, 211, 212, 213, 214],
],
31: [
"hextetrahedral",
"cubic",
["-43m"],
"non-centrosymmetric",
[215, 216, 217, 218, 219, 220],
],
32: [
"hexoctahedral",
"cubic",
["m-3m"],
"centrosymmetric",
[221, 222, 223, 224, 225, 226, 227, 228, 229, 230],
],
}
[docs]
CRYSTAL_CLASSES_NOSG = {
1: ["pedial", "triclinic", ["1"], "enantiomorphic-polar"],
2: ["pinacoidal", "triclinic", ["-1"], "centrosymmetric"],
3: ["sphenoidal", "monoclinic", ["2"], "enantiomorphic-polar"],
4: ["domatic", "monoclinic", ["m"], "polar"],
5: ["prismatic", "monoclinic", ["2/m"], "centrosymmetric"],
6: ["rhombic-disphenoidal", "orthorhombic", ["222"], "enantiomorphic"],
7: ["rhombic-pyramidal", "orthorhombic", ["mm2"], "polar"],
8: ["rhombic-dipyramidal", "orthorhombic", ["mmm"], "centrosymmetric"],
9: ["tetragonal-pyramidal", "tetragonal", ["4"], "enantiomorphic-polar"],
10: ["tetragonal-disphenoidal", "tetragonal", ["-4"], "non-centrosymmetric"],
11: ["tetragonal-dipyramidal", "tetragonal", ["4/m"], "centrosymmetric"],
12: ["tetragonal-trapezohedral", "tetragonal", ["422"], "enantiomorphic"],
13: ["ditetragonal-pyramidal", "tetragonal", ["4mm"], "polar"],
14: [
"tetragonal-scalenohedral",
"tetragonal",
["-42m", "-4m2"],
"non-centrosymmetric",
],
15: ["ditetragonal-dipyramidal", "tetragonal", ["4/mmm"], "centrosymmetric"],
16: ["trigonal-pyramidal", "trigonal", ["3"], "enantiomorphic-polar"],
17: ["rhombohedral", "trigonal", ["-3"], "centrosymmetric"],
18: [
"trigonal-trapezohedral",
"trigonal",
["32", "321", "312"],
"enantiomorphic",
],
19: ["ditrigonal-pyramidal", "trigonal", ["3m", "3m1", "31m"], "polar"],
20: [
"ditrigonal-scalenohedral",
"trigonal",
["-3m", "-3m1", "-31m"],
"centrosymmetric",
],
21: ["hexagonal-pyramidal", "hexagonal", ["6"], "enantiomorphic-polar"],
22: ["trigonal-dipyramidal", "hexagonal", ["-6"], "non-centrosymmetric"],
23: ["hexagonal-dipyramidal", "hexagonal", ["6/m"], "centrosymmetric"],
24: ["hexagonal-trapezohedral", "hexagonal", ["622"], "enantiomorphic"],
25: ["dihexagonal-pyramidal", "hexagonal", ["6mm"], "polar"],
26: [
"ditrigonal-dipyramidal",
"hexagonal",
["-6m2", "-62m"],
"non-centrosymmetric",
],
27: ["dihexagonal-dipyramidal", "hexagonal", ["6/mmm"], "centrosymmetric"],
28: ["tetartoidal", "cubic", ["23"], "enantiomorphic"],
29: ["diploidal", "cubic", ["m-3"], "centrosymmetric"],
30: ["gyroidal", "cubic", ["432"], "enantiomorphic"],
31: ["hextetrahedral", "cubic", ["-43m"], "non-centrosymmetric"],
32: ["hexoctahedral", "cubic", ["m-3m"], "centrosymmetric"],
}
# See: https://en.wikipedia.org/wiki/Crystal_system#Crystal_classes
# See: http://pd.chem.ucl.ac.uk/pdnn/symm2/group32.htm
# Each item in the dictionary contains a list of:
# - point symmetry name
# - crystal system indices with the point symmetry
# - crystal class indices with the point symmetry
[docs]
POINT_SYMMETRIES = {
1: ["enantiomorphic-polar", [1, 2, 4, 5, 6], [1, 3, 9, 16, 21]],
2: [
"centrosymmetric",
[1, 2, 3, 4, 5, 6, 7],
[2, 5, 8, 11, 15, 17, 20, 23, 27, 29, 32],
],
3: ["polar", [2, 3, 4, 5, 6], [4, 7, 13, 19, 25]],
4: ["enantiomorphic", [3, 4, 5, 6, 7], [6, 12, 18, 24, 28, 30]],
5: ["non-centrosymmetric", [4, 6, 7], [10, 14, 22, 26, 31]],
}
[docs]
POINT_SYMMETRIES_MINIMAL = {
1: "enantiomorphic-polar",
2: "centrosymmetric",
3: "polar",
4: "enantiomorphic",
5: "non-centrosymmetric",
}
# Point group of each space group, from pymatgen
# See: ./scripts/pymatgen/pg_of_all_sg.py
# Each item in the dictionary contains a list of:
# - point group as in pymatgen
# - crystal class index of the point group
# - crystal system index
# - point symmetry index
[docs]
SPACE_GROUPS = {
1: ["1", 1, 1, 1],
2: ["-1", 2, 1, 2],
3: ["2", 3, 2, 1],
4: ["2", 3, 2, 1],
5: ["2", 3, 2, 1],
6: ["m", 4, 2, 3],
7: ["m", 4, 2, 3],
8: ["m", 4, 2, 3],
9: ["m", 4, 2, 3],
10: ["2/m", 5, 2, 2],
11: ["2/m", 5, 2, 2],
12: ["2/m", 5, 2, 2],
13: ["2/m", 5, 2, 2],
14: ["2/m", 5, 2, 2],
15: ["2/m", 5, 2, 2],
16: ["222", 6, 3, 4],
17: ["222", 6, 3, 4],
18: ["222", 6, 3, 4],
19: ["222", 6, 3, 4],
20: ["222", 6, 3, 4],
21: ["222", 6, 3, 4],
22: ["222", 6, 3, 4],
23: ["222", 6, 3, 4],
24: ["222", 6, 3, 4],
25: ["mm2", 7, 3, 3],
26: ["mm2", 7, 3, 3],
27: ["mm2", 7, 3, 3],
28: ["mm2", 7, 3, 3],
29: ["mm2", 7, 3, 3],
30: ["mm2", 7, 3, 3],
31: ["mm2", 7, 3, 3],
32: ["mm2", 7, 3, 3],
33: ["mm2", 7, 3, 3],
34: ["mm2", 7, 3, 3],
35: ["mm2", 7, 3, 3],
36: ["mm2", 7, 3, 3],
37: ["mm2", 7, 3, 3],
38: ["mm2", 7, 3, 3],
39: ["mm2", 7, 3, 3],
40: ["mm2", 7, 3, 3],
41: ["mm2", 7, 3, 3],
42: ["mm2", 7, 3, 3],
43: ["mm2", 7, 3, 3],
44: ["mm2", 7, 3, 3],
45: ["mm2", 7, 3, 3],
46: ["mm2", 7, 3, 3],
47: ["mmm", 8, 3, 2],
48: ["mmm", 8, 3, 2],
49: ["mmm", 8, 3, 2],
50: ["mmm", 8, 3, 2],
51: ["mmm", 8, 3, 2],
52: ["mmm", 8, 3, 2],
53: ["mmm", 8, 3, 2],
54: ["mmm", 8, 3, 2],
55: ["mmm", 8, 3, 2],
56: ["mmm", 8, 3, 2],
57: ["mmm", 8, 3, 2],
58: ["mmm", 8, 3, 2],
59: ["mmm", 8, 3, 2],
60: ["mmm", 8, 3, 2],
61: ["mmm", 8, 3, 2],
62: ["mmm", 8, 3, 2],
63: ["mmm", 8, 3, 2],
64: ["mmm", 8, 3, 2],
65: ["mmm", 8, 3, 2],
66: ["mmm", 8, 3, 2],
67: ["mmm", 8, 3, 2],
68: ["mmm", 8, 3, 2],
69: ["mmm", 8, 3, 2],
70: ["mmm", 8, 3, 2],
71: ["mmm", 8, 3, 2],
72: ["mmm", 8, 3, 2],
73: ["mmm", 8, 3, 2],
74: ["mmm", 8, 3, 2],
75: ["4", 9, 4, 1],
76: ["4", 9, 4, 1],
77: ["4", 9, 4, 1],
78: ["4", 9, 4, 1],
79: ["4", 9, 4, 1],
80: ["4", 9, 4, 1],
81: ["-4", 10, 4, 5],
82: ["-4", 10, 4, 5],
83: ["4/m", 11, 4, 2],
84: ["4/m", 11, 4, 2],
85: ["4/m", 11, 4, 2],
86: ["4/m", 11, 4, 2],
87: ["4/m", 11, 4, 2],
88: ["4/m", 11, 4, 2],
89: ["422", 12, 4, 4],
90: ["422", 12, 4, 4],
91: ["422", 12, 4, 4],
92: ["422", 12, 4, 4],
93: ["422", 12, 4, 4],
94: ["422", 12, 4, 4],
95: ["422", 12, 4, 4],
96: ["422", 12, 4, 4],
97: ["422", 12, 4, 4],
98: ["422", 12, 4, 4],
99: ["4mm", 13, 4, 3],
100: ["4mm", 13, 4, 3],
101: ["4mm", 13, 4, 3],
102: ["4mm", 13, 4, 3],
103: ["4mm", 13, 4, 3],
104: ["4mm", 13, 4, 3],
105: ["4mm", 13, 4, 3],
106: ["4mm", 13, 4, 3],
107: ["4mm", 13, 4, 3],
108: ["4mm", 13, 4, 3],
109: ["4mm", 13, 4, 3],
110: ["4mm", 13, 4, 3],
111: ["-42m", 14, 4, 5],
112: ["-42m", 14, 4, 5],
113: ["-42m", 14, 4, 5],
114: ["-42m", 14, 4, 5],
115: ["-4m2", 14, 4, 5],
116: ["-4m2", 14, 4, 5],
117: ["-4m2", 14, 4, 5],
118: ["-4m2", 14, 4, 5],
119: ["-4m2", 14, 4, 5],
120: ["-4m2", 14, 4, 5],
121: ["-42m", 14, 4, 5],
122: ["-42m", 14, 4, 5],
123: ["4/mmm", 15, 4, 2],
124: ["4/mmm", 15, 4, 2],
125: ["4/mmm", 15, 4, 2],
126: ["4/mmm", 15, 4, 2],
127: ["4/mmm", 15, 4, 2],
128: ["4/mmm", 15, 4, 2],
129: ["4/mmm", 15, 4, 2],
130: ["4/mmm", 15, 4, 2],
131: ["4/mmm", 15, 4, 2],
132: ["4/mmm", 15, 4, 2],
133: ["4/mmm", 15, 4, 2],
134: ["4/mmm", 15, 4, 2],
135: ["4/mmm", 15, 4, 2],
136: ["4/mmm", 15, 4, 2],
137: ["4/mmm", 15, 4, 2],
138: ["4/mmm", 15, 4, 2],
139: ["4/mmm", 15, 4, 2],
140: ["4/mmm", 15, 4, 2],
141: ["4/mmm", 15, 4, 2],
142: ["4/mmm", 15, 4, 2],
143: ["3", 16, 5, 1],
144: ["3", 16, 5, 1],
145: ["3", 16, 5, 1],
146: ["3", 16, 5, 1],
147: ["-3", 17, 5, 2],
148: ["-3", 17, 5, 2],
149: ["312", 18, 5, 4],
150: ["321", 18, 5, 4],
151: ["312", 18, 5, 4],
152: ["321", 18, 5, 4],
153: ["312", 18, 5, 4],
154: ["321", 18, 5, 4],
155: ["32", 18, 5, 4],
156: ["3m1", 19, 5, 3],
157: ["31m", 19, 5, 3],
158: ["3m1", 19, 5, 3],
159: ["31m", 19, 5, 3],
160: ["3m", 19, 5, 3],
161: ["3m", 19, 5, 3],
162: ["-31m", 20, 5, 2],
163: ["-31m", 20, 5, 2],
164: ["-3m1", 20, 5, 2],
165: ["-3m1", 20, 5, 2],
166: ["-3m", 20, 5, 2],
167: ["-3m", 20, 5, 2],
168: ["6", 21, 6, 1],
169: ["6", 21, 6, 1],
170: ["6", 21, 6, 1],
171: ["6", 21, 6, 1],
172: ["6", 21, 6, 1],
173: ["6", 21, 6, 1],
174: ["-6", 22, 6, 5],
175: ["6/m", 23, 6, 2],
176: ["6/m", 23, 6, 2],
177: ["622", 24, 6, 4],
178: ["622", 24, 6, 4],
179: ["622", 24, 6, 4],
180: ["622", 24, 6, 4],
181: ["622", 24, 6, 4],
182: ["622", 24, 6, 4],
183: ["6mm", 25, 6, 3],
184: ["6mm", 25, 6, 3],
185: ["6mm", 25, 6, 3],
186: ["6mm", 25, 6, 3],
187: ["-6m2", 26, 6, 5],
188: ["-6m2", 26, 6, 5],
189: ["-62m", 26, 6, 5],
190: ["-62m", 26, 6, 5],
191: ["6/mmm", 27, 6, 2],
192: ["6/mmm", 27, 6, 2],
193: ["6/mmm", 27, 6, 2],
194: ["6/mmm", 27, 6, 2],
195: ["23", 28, 7, 4],
196: ["23", 28, 7, 4],
197: ["23", 28, 7, 4],
198: ["23", 28, 7, 4],
199: ["23", 28, 7, 4],
200: ["m-3", 29, 7, 2],
201: ["m-3", 29, 7, 2],
202: ["m-3", 29, 7, 2],
203: ["m-3", 29, 7, 2],
204: ["m-3", 29, 7, 2],
205: ["m-3", 29, 7, 2],
206: ["m-3", 29, 7, 2],
207: ["432", 30, 7, 4],
208: ["432", 30, 7, 4],
209: ["432", 30, 7, 4],
210: ["432", 30, 7, 4],
211: ["432", 30, 7, 4],
212: ["432", 30, 7, 4],
213: ["432", 30, 7, 4],
214: ["432", 30, 7, 4],
215: ["-43m", 31, 7, 5],
216: ["-43m", 31, 7, 5],
217: ["-43m", 31, 7, 5],
218: ["-43m", 31, 7, 5],
219: ["-43m", 31, 7, 5],
220: ["-43m", 31, 7, 5],
221: ["m-3m", 32, 7, 2],
222: ["m-3m", 32, 7, 2],
223: ["m-3m", 32, 7, 2],
224: ["m-3m", 32, 7, 2],
225: ["m-3m", 32, 7, 2],
226: ["m-3m", 32, 7, 2],
227: ["m-3m", 32, 7, 2],
228: ["m-3m", 32, 7, 2],
229: ["m-3m", 32, 7, 2],
230: ["m-3m", 32, 7, 2],
}
[docs]
SPACE_GROUPS_MINIMAL = {
1: "1",
2: "-1",
3: "2",
4: "2",
5: "2",
6: "m",
7: "m",
8: "m",
9: "m",
10: "2/m",
11: "2/m",
12: "2/m",
13: "2/m",
14: "2/m",
15: "2/m",
16: "222",
17: "222",
18: "222",
19: "222",
20: "222",
21: "222",
22: "222",
23: "222",
24: "222",
25: "mm2",
26: "mm2",
27: "mm2",
28: "mm2",
29: "mm2",
30: "mm2",
31: "mm2",
32: "mm2",
33: "mm2",
34: "mm2",
35: "mm2",
36: "mm2",
37: "mm2",
38: "mm2",
39: "mm2",
40: "mm2",
41: "mm2",
42: "mm2",
43: "mm2",
44: "mm2",
45: "mm2",
46: "mm2",
47: "mmm",
48: "mmm",
49: "mmm",
50: "mmm",
51: "mmm",
52: "mmm",
53: "mmm",
54: "mmm",
55: "mmm",
56: "mmm",
57: "mmm",
58: "mmm",
59: "mmm",
60: "mmm",
61: "mmm",
62: "mmm",
63: "mmm",
64: "mmm",
65: "mmm",
66: "mmm",
67: "mmm",
68: "mmm",
69: "mmm",
70: "mmm",
71: "mmm",
72: "mmm",
73: "mmm",
74: "mmm",
75: "4",
76: "4",
77: "4",
78: "4",
79: "4",
80: "4",
81: "-4",
82: "-4",
83: "4/m",
84: "4/m",
85: "4/m",
86: "4/m",
87: "4/m",
88: "4/m",
89: "422",
90: "422",
91: "422",
92: "422",
93: "422",
94: "422",
95: "422",
96: "422",
97: "422",
98: "422",
99: "4mm",
100: "4mm",
101: "4mm",
102: "4mm",
103: "4mm",
104: "4mm",
105: "4mm",
106: "4mm",
107: "4mm",
108: "4mm",
109: "4mm",
110: "4mm",
111: "-42m",
112: "-42m",
113: "-42m",
114: "-42m",
115: "-4m2",
116: "-4m2",
117: "-4m2",
118: "-4m2",
119: "-4m2",
120: "-4m2",
121: "-42m",
122: "-42m",
123: "4/mmm",
124: "4/mmm",
125: "4/mmm",
126: "4/mmm",
127: "4/mmm",
128: "4/mmm",
129: "4/mmm",
130: "4/mmm",
131: "4/mmm",
132: "4/mmm",
133: "4/mmm",
134: "4/mmm",
135: "4/mmm",
136: "4/mmm",
137: "4/mmm",
138: "4/mmm",
139: "4/mmm",
140: "4/mmm",
141: "4/mmm",
142: "4/mmm",
143: "3",
144: "3",
145: "3",
146: "3",
147: "-3",
148: "-3",
149: "312",
150: "321",
151: "312",
152: "321",
153: "312",
154: "321",
155: "32",
156: "3m1",
157: "31m",
158: "3m1",
159: "31m",
160: "3m",
161: "3m",
162: "-31m",
163: "-31m",
164: "-3m1",
165: "-3m1",
166: "-3m",
167: "-3m",
168: "6",
169: "6",
170: "6",
171: "6",
172: "6",
173: "6",
174: "-6",
175: "6/m",
176: "6/m",
177: "622",
178: "622",
179: "622",
180: "622",
181: "622",
182: "622",
183: "6mm",
184: "6mm",
185: "6mm",
186: "6mm",
187: "-6m2",
188: "-6m2",
189: "-62m",
190: "-62m",
191: "6/mmm",
192: "6/mmm",
193: "6/mmm",
194: "6/mmm",
195: "23",
196: "23",
197: "23",
198: "23",
199: "23",
200: "m-3",
201: "m-3",
202: "m-3",
203: "m-3",
204: "m-3",
205: "m-3",
206: "m-3",
207: "432",
208: "432",
209: "432",
210: "432",
211: "432",
212: "432",
213: "432",
214: "432",
215: "-43m",
216: "-43m",
217: "-43m",
218: "-43m",
219: "-43m",
220: "-43m",
221: "m-3m",
222: "m-3m",
223: "m-3m",
224: "m-3m",
225: "m-3m",
226: "m-3m",
227: "m-3m",
228: "m-3m",
229: "m-3m",
230: "m-3m",
}