Group Settings ============== For the output 3D structures, PyXtal uses the conventional standard cell (same as `Bilbao `_). Below are the links for each set. - `Space group `_ - `Layer group `_ - `Rod group `_ One can conveniently access the list of crystallographic point groups, 1D rod, 2D layer groups and 3D space groups by changing the ``dim`` flag. .. code-block:: Python >>> from pyxtal.symmetry import Group >>> g=Group.list_groups(dim=0) point_group 1 C1 2 Ci 3 C2 ... 56 Ih 57 C* 58 C*h Space Group ----------- By default, pyxtal follows the standard according to the Volume A of International Tables for Crystallography. They are defined as: unique axis b setting, cell choice 1 for monoclinic groups, hexagonal axes setting for rhombohedral groups, and origin choice 2 (origin in -1) for the centrosymmetric groups listed with respect to two origins. The relation between the standard space group and hall numbers are shown as follows, .. code-block:: Python pyxtal_hall_numbers = [ 1, 2, 3, 6, 9, 18, 21, 30, 39, 57, 60, 63, 72, 81, 90, 108, 109, 112, 115, 116, 119, 122, 123, 124, 125, 128, 134, 137, 143, 149, 155, 161, 164, 170, 173, 176, 182, 185, 191, 197, 203, 209, 212, 215, 218, 221, 227, 229, 230, 234, 239, 245, 251, 257, 263, 266, 269, 275, 279, 284, 290, 292, 298, 304, 310, 313, 316, 323, 334, 336, 337, 338, 341, 343, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 360, 362, 363, 365, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 400, 401, 403, 405, 406, 407, 409, 411, 412, 413, 415, 417, 418, 419, 421, 423, 424, 425, 427, 429, 430, 431, 432, 433, 435, 436, 438, 439, 440, 441, 442, 443, 444, 446, 447, 448, 449, 450, 452, 454, 455, 456, 457, 458, 460, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 494, 496, 497, 499, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517, 519, 520, 522, 523, 524, 526, 528, 529, 530] However, in some programs like Spglib, when converting from space group to Hall numbers, the first description of the space-group type in International Tables for Crystallography) is chosen. In this case, the Hall number ``525`` (instead of ``526``) will be chosen for the space group ``227``. .. code-block:: Python spglib_hall_numbers = [ 1, 2, 3, 6, 9, 18, 21, 30, 39, 57, 60, 63, 72, 81, 90, 108, 109, 112, 115, 116, 119, 122, 123, 124, 125, 128, 134, 137, 143, 149, 155, 161, 164, 170, 173, 176, 182, 185, 191, 197, 203, 209, 212, 215, 218, 221, 227, 228, 230, 233, 239, 245, 251, 257, 263, 266, 269, 275, 278, 284, 290, 292, 298, 304, 310, 313, 316, 322, 334, 335, 337, 338, 341, 343, 349, 350, 351, 352, 353, 354, 355, 356, 357, 358, 359, 361, 363, 364, 366, 367, 368, 369, 370, 371, 372, 373, 374, 375, 376, 377, 378, 379, 380, 381, 382, 383, 384, 385, 386, 387, 388, 389, 390, 391, 392, 393, 394, 395, 396, 397, 398, 399, 400, 401, 402, 404, 406, 407, 408, 410, 412, 413, 414, 416, 418, 419, 420, 422, 424, 425, 426, 428, 430, 431, 432, 433, 435, 436, 438, 439, 440, 441, 442, 443, 444, 446, 447, 448, 449, 450, 452, 454, 455, 456, 457, 458, 460, 462, 463, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 474, 475, 476, 477, 478, 479, 480, 481, 482, 483, 484, 485, 486, 487, 488, 489, 490, 491, 492, 493, 494, 495, 497, 498, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 510, 511, 512, 513, 514, 515, 516, 517, 518, 520, 521, 523, 524, 525, 527, 529, 530] Layer Group ----------- For 2D structures, we use unique axis c for monoclinic layer groups 3-7, and unique axis a for layer groups 8-18. When two origin choices are available, we use origin choice 1. We always choose c as the non-periodic axis. Rod Group --------- For 1D structures, we use unique axis a for monoclinic Rod groups 3-7, and unique axis c for Rod groups 8-12. When two settings are available for a group, we use the 1st setting. We always choose c as the periodic axis. Point Group ----------- For point group structures, we use unique axis c for all groups except the polyhedral groups ``T, Th, O, Td, Oh, I, and Ih``. For all of these groups, we place the 2-fold rotation about the z axis and a 3-fold rotation about the (x,x,x) axis. For ``I`` and ``Ih``, we use a 5-fold rotation about the axis (1, :math:`\tau`, 0), where :math:`\tau` is the golden ratio 1.618. All supported point groups, listed by number: +------------+------------+-----------+-----------+ | 1: C1 | 2: Ci | 3: C2 | 4: Cs | +------------+------------+-----------+-----------+ | 5: C2h | 6: D2 | 7: C2v | 8: D2h | +------------+------------+-----------+-----------+ | 9: C4 | 10: S4 | 11: C4h | 12: D4 | +------------+------------+-----------+-----------+ | 13: C4v | 14: D2d | 15: D4h | 16: C3 | +------------+------------+-----------+-----------+ | 17: C3i | 18: D3 | 19: C3v | 20: D3d | +------------+------------+-----------+-----------+ | 21: C6 | 22: C3h | 23: C6h | 24: D6 | +------------+------------+-----------+-----------+ | 25: C6v | 26: D3h | 27: D6h | 28: T | +------------+------------+-----------+-----------+ | 29: Th | 30: O | 31: Td | 32: Oh | +------------+------------+-----------+-----------+ | 33: C5 | 34: C7 | 35: C8 | 36: D5 | +------------+------------+-----------+-----------+ | 37: D7 | 38: D8 | 39: C5v | 40: C7v | +------------+------------+-----------+-----------+ | 41: C8v | 42: C5h | 43: D5h | 44: D7h | +------------+------------+-----------+-----------+ | 45: D8h | 46: D4d | 47: D5d | 48: D6d | +------------+------------+-----------+-----------+ | 49: D7d | 50: D8d | 51: S6 | 52: S8 | +------------+------------+-----------+-----------+ | 53: S10 | 54: S12 | 55: I | 56: Ih | +------------+------------+-----------+-----------+ | 57: C* | 58: C*h | | | +------------+------------+-----------+-----------+ In addition to the 32 crystallographic point group , we add the following finite non-crystallographic point groups: ``Cn, Cnh, Cnv, Sn, Cni, Dn, Dnh, Dnd.`` where n should be replaced by an integer. I and Ih, which are the icosahedral and full icosahedral groups, are particularly useful (Buckminsterfullerene, for example has point group symmetry ``Ih``). Finally, the infinite rotational and dihedral point groups ``C*`` and ``C*h`` can be used for generating linear structures. ``C*h`` will have mirror symmetry, while ``C*`` will not.