International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2006). Vol. B, ch. 1.4, pp. 150-161   | 1 | 2 |
https://doi.org/10.1107/97809553602060000552

Appendix A1.4.4. Crystallographic space groups in reciprocal space

U. Shmuelia

[link]

Table A1.4.4.1| top | pdf |
Crystallographic space groups in reciprocal space

The table entries are described in detail in Section 1.4.4.1[link]. The general format of an entry is [(n)\;{\bf h}^T{\bi P}_n: -{\bf h}^T{\bf t}_n]or[(n)\;{\bf h}^T{\bi P}_n:,] according as the phase-shift part of the entry is nonzero or zero modolo [2\pi{}], respectively.

Notes:

  • (1) For centrosymmetric space groups with the centre located at the unit-cell origin only those entries are given which correspond to symmetry operations not related by inversion. If the origin in such space groups is chosen elsewhere, all the entries corresponding to the operations of the point group are presented.

  • (2) For trigonal and hexagonal space groups referred to hexagonal axes the Miller–Bravais indices hkil are employed, and for the rhombohedral space groups referred to rhombohedral axes the indices are denoted by hkl (cf. IT I, 1952[link]).

Point group: 1 Triclinic Laue group: [{\bf {\overline{1}}}]
[P1] No. 1 (1)
(1) [hkl]:

Point group: [{\bf {\overline{1}}}] Triclinic Laue group: [{\bf {\overline{1}}}]
[P\overline{1}] No. 2 (2)
(1) [hkl]:

Point group: 2 Monoclinic Laue group: 2/m
[P2] [P121] Unique axis b No. 3 (3)
(1) [hkl]: (2) [\overline{h}k\overline{l}]:
 
[P2] [P112] Unique axis c No. 3 (4)
(1) [hkl]: (2) [\overline{h}\overline{k}l]:
 
[P2_{1}] [P12_{1}1] Unique axis b No. 4 (5)
(1) [hkl]: (2) [\overline{h}k\overline{l}]: −010/2
 
[P2_{1}] [P112_{1}] Unique axis c No. 4 (6)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −001/2
 
[C2] [C121] Unique axis b No. 5 (7)
(1) [hkl]: (2) [\overline{h}k\overline{l}]:
 
[C2] [A121] Unique axis b No. 5 (8)
(1) [hkl]: (2) [\overline{h}k\overline{l}]:
 
[C2] [I121] Unique axis b No. 5 (9)
(1) [hkl]: (2) [\overline{h}k\overline{l}]:
 
[C2] [A112] Unique axis c No. 5 (10)
(1) [hkl]: (2) [\overline{h}\overline{k}l]:
 
[C2] [B112] Unique axis c No. 5 (11)
(1) [hkl]: (2) [\overline{h}\overline{k}l]:
 
[C2] [I112 ] Unique axis c No. 5 (12)
(1) [hkl]: (2) [\overline{h}\overline{k}l]:

Point group: m Monoclinic Laue group: 2/m
[Pm] [P1m1] Unique axis b No. 6 (13)
(1) [hkl]: (2) [h\overline{k}l]:
 
[Pm] [P11m] Unique axis c No. 6 (14)
(1) [hkl]: (2) [hk\overline{l}]:
 
[Pc] [P1c1] Unique axis b No. 7 (15)
(1) [hkl]: (2) [h\overline{k}l]: −001/2
 
[Pc] [P1n1] Unique axis b No. 7 (16)
(1) [hkl]: (2) [h\overline{k}l]: −101/2
 
[Pc] [P1a1] Unique axis b No. 7 (17)
(1) [hkl]: (2) [h\overline{k}l]: −100/2
 
[Pc] [P11a] Unique axis c No. 7 (18)
(1) [hkl]: (2) [hk\overline{l}]: −100/2
 
[Pc] [P11n] Unique axis c No. 7 (19)
(1) [hkl]: (2) [hk\overline{l}]: −110/2
 
[Pc] [P11b] Unique axis c No. 7 (20)
(1) [hkl]: (2) [hk\overline{l}]: −010/2
 
[Cm] [C1m1] Unique axis b No. 8 (21)
(1) [hkl]: (2) [h\overline{k}l]:
 
[Cm] [A1m1] Unique axis b No. 8 (22)
(1) [hkl]: (2) [h\overline{k}l]:
 
[Cm] [I1m1] Unique axis b No. 8 (23)
(1) [hkl]: (2) [h\overline{k}l]:
 
[Cm] [A11m] Unique axis c No. 8 (24)
(1) [hkl]: (2) [hk\overline{l}]:
 
[Cm] [B11m] Unique axis c No. 8 (25)
(1) [hkl]: (2) [hk\overline{l}]:
 
[Cm] [I11m] Unique axis c No. 8 (26)
(1) [hkl]: (2) [hk\overline{l}]:
 
[Cc] [C1c1] Unique axis b No. 9 (27)
(1) [hkl]: (2) [h\overline{k}l]: −001/2
 
[Cc] [A1n1] Unique axis b No. 9 (28)
(1) [hkl]: (2) [h\overline{k}l]: −101/2
 
[Cc] [I1a1] Unique axis b No. 9 (29)
(1) [hkl]: (2) [h\overline{k}l]: −100/2
 
[Cc] [A11a] Unique axis c No. 9 (30)
(1) [hkl]: (2) [hk\overline{l}]: −100/2
 
[Cc] [B11n] Unique axis c No. 9 (31)
(1) [hkl]: (2) [hk\overline{l}]: −110/2
 
[Cc] [I11b] Unique axis c No. 9 (32)
(1) [hkl]: (2) [hk\overline{l}]: −010/2

Point group: 2/m Monoclinic Laue group: 2/m
[P2/m] [P12/m1] Unique axis b No. 10 (33)
(1) [hkl]: (2) [\overline{h}k\overline{l}]:
 
[P2/m] [P112/m] Unique axis c No. 10 (34)
(1) [hkl]: (2) [\overline{h}\overline{k}l]:
 
[P2_{1}/m] [P12_{1}/m1] Unique axis b No. 11 (35)
(1) [hkl]: (2) [\overline{h}k\overline{l}]: −010/2
 
[P2_{1}/m] [P112_{1}/m] Unique axis c No. 11 (36)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −001/2
 
[C2/m] [C12/m1] Unique axis b No. 12 (37)
(1) [hkl]: (2) [\overline{h}k\overline{l}]:
 
[C2/m] [A12/m1] Unique axis b No. 12 (38)
(1) [hkl]: (2) [\overline{h}k\overline{l}]:
 
[C2/m] [I12/m1] Unique axis b No. 12 (39)
(1) [hkl]: (2) [\overline{h}k\overline{l}]:
 
[C2/m] [A112/m] Unique axis c No. 12 (40)
(1) [hkl]: (2) [\overline{h}\overline{k}l]:
 
[C2/m] [B112/m] Unique axis c No. 12 (41)
(1) [hkl]: (2) [\overline{h}\overline{k}l]:
 
[C2/m] [I112/m] Unique axis c No. 12 (42)
(1) [hkl]: (2) [\overline{h}\overline{k}l]:
 
[P2/c] [P12/c1] Unique axis b No. 13 (43)
(1) [hkl]: (2) [\overline{h}k\overline{l}]: −001/2
 
[P2/c] [P12/n1] Unique axis b No. 13 (44)
(1) [hkl]: (2) [\overline{h}k\overline{l}]: −101/2
 
[P2/c] [P12/a1] Unique axis b No. 13 (45)
(1) [hkl]: (2) [\overline{h}k\overline{l}]: −100/2
 
[P2/c] [P112/a] Unique axis c No. 13 (46)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −100/2
 
[P2/c] [P112/n] Unique axis c No. 13 (47)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −110/2
 
[P2/c] [P112/b] Unique axis c No. 13 (48)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −010/2
 
[P2_{1}/c] [P12_{1}/c1] Unique axis b No. 14 (49)
(1) [hkl]: (2) [\overline{h}k\overline{l}]: −011/2
 
[P2_{1}/c] [P12_{1}/n1] Unique axis b No. 14 (50)
(1) [hkl]: (2) [\overline{h}k\overline{l}]: −111/2
 
[P2_{1}/c] [P12_{1}/a1] Unique axis b No. 14 (51)
(1) [hkl]: (2) [\overline{h}k\overline{l}]: −110/2
 
[P2_{1}/c] [P112_{1}/a] Unique axis c No. 14 (52)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −101/2
 
[P2_{1}/c] [P112_{1}/n] Unique axis c No. 14 (53)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −111/2
 
[P2_{1}/c] [P112_{1}/b] Unique axis c No. 14 (54)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −011/2
 
[C2/c] [C12/c1] Unique axis b No. 15 (55)
(1) [hkl]: (2) [\overline{h}k\overline{l}]: −001/2
 
[C2/c] [A12/n1] Unique axis b No. 15 (56)
(1) [hkl]: (2) [\overline{h}k\overline{l}]: −101/2
 
[C2/c] [I12/a1] Unique axis b No. 15 (57)
(1) [hkl]: (2) [\overline{h}k\overline{l}]: −100/2
 
[C2/c] [A112/a] Unique axis c No. 15 (58)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −100/2
 
[C2/c] [B112/n] Unique axis c No. 15 (59)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −110/2
 
[C2/c] [I112/b] Unique axis c No. 15 (60)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −010/2

Point group: 222 Orthorhombic Laue group: mmm
[P222] No. 16 (61)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
 
[P222_{1}] No. 17 (62)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −001/2 (3) [\overline{h}k\overline{l}]: −001/2 (4) [h\overline{k}\overline{l}]:
 
[P2_{1}2_{1}2] No. 18 (63)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: −110/2 (4) [h\overline{k}\overline{l}]: −110/2
 
[P2_{1}2_{1}2_{1}] No. 19 (64)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −101/2 (3) [\overline{h}k\overline{l}]: −011/2 (4) [h\overline{k}\overline{l}]: −110/2
 
[C222_{1}] No. 20 (65)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −001/2 (3) [\overline{h}k\overline{l}]: −001/2 (4) [h\overline{k}\overline{l}]:
 
[C222] No. 21 (66)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
 
[F222] No. 22 (67)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
 
[I222] No. 23 (68)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
 
[I2_{1}2_{1}2_{1}] No. 24 (69)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −101/2 (3) [\overline{h}k\overline{l}]: −011/2 (4) [h\overline{k}\overline{l}]: −110/2

Point group: mm2 Orthorhombic Laue group: mmm
[Pmm2] No. 25 (70)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [h\overline{k}l]: (4) [\overline{h}kl]:
 
[Pmc2_{1}] No. 26 (71)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −001/2 (3) [h\overline{k}l]: −001/2 (4) [\overline{h}kl]:
 
[Pcc2] No. 27 (72)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [h\overline{k}l]: −001/2 (4) [\overline{h}kl]: −001/2
 
[Pma2] No. 28 (73)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [h\overline{k}l]: −100/2 (4) [\overline{h}kl]: −100/2
 
[Pca2_{1}] No. 29 (74)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −001/2 (3) [h\overline{k}l]: −100/2 (4) [\overline{h}kl]: −101/2
 
[Pnc2] No. 30 (75)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [h\overline{k}l]: −011/2 (4) [\overline{h}kl]: −011/2
 
[Pmn2_{1}] No. 31 (76)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −101/2 (3) [h\overline{k}l]: −101/2 (4) [\overline{h}kl]:
 
[Pba2] No. 32 (77)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [h\overline{k}l]: −110/2 (4) [\overline{h}kl]: −110/2
 
[Pna2_{1}] No. 33 (78)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −001/2 (3) [h\overline{k}l]: −110/2 (4) [\overline{h}kl]: −111/2
 
[Pnn2] No. 34 (79)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [h\overline{k}l]: −111/2 (4) [\overline{h}kl]: −111/2
 
[Cmm2] No. 35 (80)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [h\overline{k}l]: (4) [\overline{h}kl]:
 
[Cmc2_{1}] No. 36 (81)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −001/2 (3) [h\overline{k}l]: −001/2 (4) [\overline{h}kl]:
 
[Ccc2] No. 37 (82)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [h\overline{k}l]: −001/2 (4) [\overline{h}kl]: −001/2
 
[Amm2] No. 38 (83)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [h\overline{k}l]: (4) [\overline{h}kl]:
 
[Abm2] No. 39 (84)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [h\overline{k}l]: −010/2 (4) [\overline{h}kl]: −010/2
 
[Ama2] No. 40 (85)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [h\overline{k}l]: −100/2 (4) [\overline{h}kl]: −100/2
 
[Aba2] No. 41 (86)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [h\overline{k}l]: −110/2 (4) [\overline{h}kl]: −110/2
 
[Fmm2] No. 42 (87)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [h\overline{k}l]: (4) [\overline{h}kl]:
 
[Fdd2] No. 43 (88)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [h\overline{k}l]: −313/4 (4) [\overline{h}kl]: −133/4
 
[Imm2] No. 44 (89)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [h\overline{k}l]: (4) [\overline{h}kl]:
 
[Iba2] No. 45 (90)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [h\overline{k}l]: −110/2 (4) [\overline{h}kl]: −110/2
 
[Ima2] No. 46 (91)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [h\overline{k}l]: −100/2 (4) [\overline{h}kl]: −100/2

Point group: mmm Orthorhombic Laue group: mmm
[Pmmm] No. 47 (92)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
 
[Pnnn] Origin 1 No. 48 (93)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
(5) [\overline{h}\overline{k}\overline{l}]: −111/2 (6) [hk\overline{l}]: −111/2 (7) [h\overline{k}l]: −111/2 (8) [\overline{h}kl]: −111/2
 
[Pnnn] Origin 2 No. 48 (94)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −110/2 (3) [\overline{h}k\overline{l}]: −101/2 (4) [h\overline{k}\overline{l}]: −011/2
 
[Pccm] No. 49 (95)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: −001/2 (4) [h\overline{k}\overline{l}]: −001/2
 
[Pban] Origin 1 No. 50 (96)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
(5) [\overline{h}\overline{k}\overline{l}]: −110/2 (6) [hk\overline{l}]: −110/2 (7) [h\overline{k}l]: −110/2 (8) [\overline{h}kl]: −110/2
 
[Pban] Origin 2 No. 50 (97)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −110/2 (3) [\overline{h}k\overline{l}]: −100/2 (4) [h\overline{k}\overline{l}]: −010/2
 
[Pmma] No. 51 (98)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −100/2 (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]: −100/2
 
[Pnna] No. 52 (99)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −100/2 (3) [\overline{h}k\overline{l}]: −111/2 (4) [h\overline{k}\overline{l}]: −011/2
 
[Pmna] No. 53 (100)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −101/2 (3) [\overline{h}k\overline{l}]: −101/2 (4) [h\overline{k}\overline{l}]:
 
[Pcca] No. 54 (101)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −100/2 (3) [\overline{h}k\overline{l}]: −001/2 (4) [h\overline{k}\overline{l}]: −101/2
 
[Pbam] No. 55 (102)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: −110/2 (4) [h\overline{k}\overline{l}]: −110/2
 
[Pccn] No. 56 (103)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −110/2 (3) [\overline{h}k\overline{l}]: −011/2 (4) [h\overline{k}\overline{l}]: −101/2
 
[Pbcm] No. 57 (104)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −001/2 (3) [\overline{h}k\overline{l}]: −011/2 (4) [h\overline{k}\overline{l}]: −010/2
 
[Pnnm] No. 58 (105)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: −111/2 (4) [h\overline{k}\overline{l}]: −111/2
 
[Pmmn] Origin 1 No. 59 (106)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: −110/2 (4) [h\overline{k}\overline{l}]: −110/2
(5) [\overline{h}\overline{k}\overline{l}]: −110/2 (6) [hk\overline{l}]: −110/2 (7) [h\overline{k}l]: (8) [\overline{h}kl]:
 
[Pmmn] Origin 2 No. 59 (107)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −110/2 (3) [\overline{h}k\overline{l}]: −010/2 (4) [h\overline{k}\overline{l}]: −100/2
 
[Pbcn] No. 60 (108)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −111/2 (3) [\overline{h}k\overline{l}]: −001/2 (4) [h\overline{k}\overline{l}]: −110/2
 
[Pbca] No. 61 (109)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −101/2 (3) [\overline{h}k\overline{l}]: −011/2 (4) [h\overline{k}\overline{l}]: −110/2
 
[Pnma] No. 62 (110)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −101/2 (3) [\overline{h}k\overline{l}]: −010/2 (4) [h\overline{k}\overline{l}]: −111/2
 
[Cmcm] No. 63 (111)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −001/2 (3) [\overline{h}k\overline{l}]: −001/2 (4) [h\overline{k}\overline{l}]:
 
[Cmca] No. 64 (112)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −011/2 (3) [\overline{h}k\overline{l}]: −011/2 (4) [h\overline{k}\overline{l}]:
 
[Cmmm] No. 65 (113)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
 
[Cccm] No. 66 (114)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: −001/2 (4) [h\overline{k}\overline{l}]: −001/2
 
[Cmma] No. 67 (115)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −010/2 (3) [\overline{h}k\overline{l}]: −010/2 (4) [h\overline{k}\overline{l}]:
 
[Ccca] Origin 1 No. 68 (116)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −110/2 (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]: −110/2
(5) [\overline{h}\overline{k}\overline{l}]: −011/2 (6) [hk\overline{l}]: −101/2 (7) [h\overline{k}l]: −011/2 (8) [\overline{h}kl]: −101/2
 
[Ccca] Origin 2 No. 68 (117)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −100/2 (3) [\overline{h}k\overline{l}]: −001/2 (4) [h\overline{k}\overline{l}]: −101/2
 
[Fmmm] No. 69 (118)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
 
[Fddd] Origin 1 No. 70 (119)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
(5) [\overline{h}\overline{k}\overline{l}]: −111/4 (6) [hk\overline{l}]: −111/4 (7) [h\overline{k}l]: −111/4 (8) [\overline{h}kl]: −111/4
 
[Fddd] Origin 2 No. 70 (120)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −330/4 (3) [\overline{h}k\overline{l}]: −303/4 (4) [h\overline{k}\overline{l}]: −033/4
 
[Immm] No. 71 (121)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
 
[Ibam] No. 72 (122)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: −110/2 (4) [h\overline{k}\overline{l}]: −110/2
 
[Ibca] No. 73 (123)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −101/2 (3) [\overline{h}k\overline{l}]: −011/2 (4) [h\overline{k}\overline{l}]: −110/2
 
[Imma] No. 74 (124)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −010/2 (3) [\overline{h}k\overline{l}]: −010/2 (4) [h\overline{k}\overline{l}]:

Point group: 4 Tetragonal Laue group: 4/m
[P4] No. 75 (125)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: (4) [\overline{k}hl]:
 
[P4_{1}] No. 76 (126)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −001/2 (3) [k\overline{h}l]: −001/4 (4) [\overline{k}hl]: −003/4
 
[P4_{2}] No. 77 (127)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: −001/2 (4) [\overline{k}hl]: −001/2
 
[P4_{3}] No. 78 (128)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −001/2 (3) [k\overline{h}l]: −003/4 (4) [\overline{k}hl]: −001/4
 
[I4] No. 79 (129)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: (4) [\overline{k}hl]:
 
[I4_{1}] No. 80 (130)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −111/2 (3) [k\overline{h}l]: −021/4 (4) [\overline{k}hl]: −203/4

Point group: [\bf{{\overline{4}}}] Tetragonal Laue group: 4/m
[P\overline{4}] No. 81 (131)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{k}h\overline{l}]: (4) [k\overline{h}\overline{l}]:
 
[I\overline{4}] No. 82 (132)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{k}h\overline{l}]: (4) [k\overline{h}\overline{l}]:

Point group: 4/m Tetragonal Laue group: 4/m
[P4/m] No. 83 (133)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: (4) [\overline{k}hl]:
 
[P4_{2}/m] No. 84 (134)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: −001/2 (4) [\overline{k}hl]: −001/2
 
[P4/n] Origin 1 No. 85 (135)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: −110/2 (4) [\overline{k}hl]: −110/2
(5) [\overline{h}\overline{k}\overline{l}]: −110/2 (6) [hk\overline{l}]: −110/2 (7) [\overline{k}h\overline{l}]: (8) [k\overline{h}\overline{l}]:
 
[P4/n] Origin 2 No. 85 (136)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −110/2 (3) [k\overline{h}l]: −100/2 (4) [\overline{k}hl]: −010/2
 
[P4_{2}/n] Origin 1 No. 86 (137)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: −111/2 (4) [\overline{k}hl]: −111/2
(5) [\overline{h}\overline{k}\overline{l}]: −111/2 (6) [hk\overline{l}]: −111/2 (7) [\overline{k}h\overline{l}]: (8) [k\overline{h}\overline{l}]:
 
[P4_{2}/n] Origin 2 No. 86 (138)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −110/2 (3) [k\overline{h}l]: −011/2 (4) [\overline{k}hl]: −101/2
 
[I4/m] No. 87 (139)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: (4) [\overline{k}hl]:
 
[I4_{1}/a] Origin 1 No. 88 (140)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −111/2 (3) [k\overline{h}l]: −021/4 (4) [\overline{k}hl]: −203/4
(5) [\overline{h}\overline{k}\overline{l}]: −021/4 (6) [hk\overline{l}]: −203/4 (7) [\overline{k}h\overline{l}]: (8) [k\overline{h}\overline{l}]: −111/2
 
[I4_{1}/a] Origin 2 No. 88 (141)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −101/2 (3) [k\overline{h}l]: −311/4 (4) [\overline{k}hl]: −333/4

Point group: 422 Tetragonal Laue group: 4/mmm
[P422] No. 89 (142)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: (4) [\overline{k}hl]:
(5) [\overline{h}k\overline{l}]: (6) [h\overline{k}\overline{l}]: (7) [kh\overline{l}]: (8) [\overline{k}\overline{h}\overline{l}]:
 
[P42_{1}2] No. 90 (143)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: −110/2 (4) [\overline{k}hl]: −110/2
(5) [\overline{h}k\overline{l}]: −110/2 (6) [h\overline{k}\overline{l}]: −110/2 (7) [kh\overline{l}]: (8) [\overline{k}\overline{h}\overline{l}]:
 
[P4_{1}22] No. 91 (144)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −001/2 (3) [k\overline{h}l]: −001/4 (4) [\overline{k}hl]: −003/4
(5) [\overline{h}k\overline{l}]: (6) [h\overline{k}\overline{l}]: −001/2 (7) [kh\overline{l}]: −003/4 (8) [\overline{k}\overline{h}\overline{l}]: −001/4
 
[P4_{1}2_{1}2] No. 92 (145)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −001/2 (3) [k\overline{h}l]: −221/4 (4) [\overline{k}hl]: −223/4
(5) [\overline{h}k\overline{l}]: −221/4 (6) [h\overline{k}\overline{l}]: −223/4 (7) [kh\overline{l}]: (8) [\overline{k}\overline{h}\overline{l}]: −001/2
 
[P4_{2}22] No. 93 (146)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: −001/2 (4) [\overline{k}hl]: −001/2
(5) [\overline{h}k\overline{l}]: (6) [h\overline{k}\overline{l}]: (7) [kh\overline{l}]: −001/2 (8) [\overline{k}\overline{h}\overline{l}]: −001/2
 
[P4_{2}2_{1}2] No. 94 (147)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: −111/2 (4) [\overline{k}hl]: −111/2
(5) [\overline{h}k\overline{l}]: −111/2 (6) [h\overline{k}\overline{l}]: −111/2 (7) [kh\overline{l}]: (8) [\overline{k}\overline{h}\overline{l}]:
 
[P4_{3}22] No. 95 (148)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −001/2 (3) [k\overline{h}l]: −003/4 (4) [\overline{k}hl]: −001/4
(5) [\overline{h}k\overline{l}]: (6) [h\overline{k}\overline{l}]: −001/2 (7) [kh\overline{l}]: −001/4 (8) [\overline{k}\overline{h}\overline{l}]: −003/4
 
[P4_{3}2_{1}2] No. 96 (149)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −001/2 (3) [k\overline{h}l]: −223/4 (4) [\overline{k}hl]: −221/4
(5) [\overline{h}k\overline{l}]: −223/4 (6) [h\overline{k}\overline{l}]: −221/4 (7) [kh\overline{l}]: (8) [\overline{k}\overline{h}\overline{l}]: −001/2
 
[I422] No. 97 (150)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: (4) [\overline{k}hl]:
(5) [\overline{h}k\overline{l}]: (6) [h\overline{k}\overline{l}]: (7) [kh\overline{l}]: (8) [\overline{k}\overline{h}\overline{l}]:
 
[I4_{1}22] No. 98 (151)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −111/2 (3) [k\overline{h}l]: −021/4 (4) [\overline{k}hl]: −203/4
(5) [\overline{h}k\overline{l}]: −203/4 (6) [h\overline{k}\overline{l}]: −021/4 (7) [kh\overline{l}]: −111/2 (8) [\overline{k}\overline{h}\overline{l}]:

Point group: 4mm Tetragonal Laue group: 4/mmm
[P4mm] No. 99 (152)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: (4) [\overline{k}hl]:
(5) [h\overline{k}l]: (6) [\overline{h}kl]: (7) [\overline{k}\overline{h}l]: (8) [khl]:
 
[P4bm] No. 100 (153)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: (4) [\overline{k}hl]:
(5) [h\overline{k}l]: −110/2 (6) [\overline{h}kl]: −110/2 (7) [\overline{k}\overline{h}l]: −110/2 (8) [khl]: −110/2
 
[P4_{2}cm] No. 101 (154)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: −001/2 (4) [\overline{k}hl]: −001/2
(5) [h\overline{k}l]: −001/2 (6) [\overline{h}kl]: −001/2 (7) [\overline{k}\overline{h}l]: (8) [khl]:
 
[P4_{2}nm] No. 102 (155)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: −111/2 (4) [\overline{k}hl]: −111/2
(5) [h\overline{k}l]: −111/2 (6) [\overline{h}kl]: −111/2 (7) [\overline{k}\overline{h}l]: (8) [khl]:
 
[P4cc] No. 103 (156)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: (4) [\overline{k}hl]:
(5) [h\overline{k}l]: −001/2 (6) [\overline{h}kl]: −001/2 (7) [\overline{k}\overline{h}l]: −001/2 (8) [khl]: −001/2
 
[P4nc] No. 104 (157)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: (4) [\overline{k}hl]:
(5) [h\overline{k}l]: −111/2 (6) [\overline{h}kl]: −111/2 (7) [\overline{k}\overline{h}l]: −111/2 (8) [khl]: −111/2
 
[P4_{2}mc] No. 105 (158)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: −001/2 (4) [\overline{k}hl]: −001/2
(5) [h\overline{k}l]: (6) [\overline{h}kl]: (7) [\overline{k}\overline{h}l]: −001/2 (8) [khl]: −001/2
 
[P4_{2}bc] No. 106 (159)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: −001/2 (4) [\overline{k}hl]: −001/2
(5) [h\overline{k}l]: −110/2 (6) [\overline{h}kl]: −110/2 (7) [\overline{k}\overline{h}l]: −111/2 (8) [khl]: −111/2
 
[I4mm] No. 107 (160)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: (4) [\overline{k}hl]:
(5) [h\overline{k}l]: (6) [\overline{h}kl]: (7) [\overline{k}\overline{h}l]: (8) [khl]:
 
[I4cm] No. 108 (161)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: (4) [\overline{k}hl]:
(5) [h\overline{k}l]: −001/2 (6) [\overline{h}kl]: −001/2 (7) [\overline{k}\overline{h}l]: −001/2 (8) [khl]: −001/2
 
[I4_{1}md] No. 109 (162)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −111/2 (3) [k\overline{h}l]: −021/4 (4) [\overline{k}hl]: −203/4
(5) [h\overline{k}l]: (6) [\overline{h}kl]: −111/2 (7) [\overline{k}\overline{h}l]: −203/4 (8) [khl]: −021/4
 
[I4_{1}cd] No. 110 (163)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −111/2 (3) [k\overline{h}l]: −021/4 (4) [\overline{k}hl]: −203/4
(5) [h\overline{k}l]: −001/2 (6) [\overline{h}kl]: −110/2 (7) [\overline{k}\overline{h}l]: −201/4 (8) [khl]: −023/4

Point group: [\bf{{\overline{4}}}]2m Tetragonal Laue group: 4/mmm
[P\overline{4}2m] No. 111 (164)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{k}h\overline{l}]: (4) [k\overline{h}\overline{l}]:
(5) [\overline{h}k\overline{l}]: (6) [h\overline{k}\overline{l}]: (7) [\overline{k}\overline{h}l]: (8) [khl]:
 
[P\overline{4}2c] No. 112 (165)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{k}h\overline{l}]: (4) [k\overline{h}\overline{l}]:
(5) [\overline{h}k\overline{l}]: −001/2 (6) [h\overline{k}\overline{l}]: −001/2 (7) [\overline{k}\overline{h}l]: −001/2 (8) [khl]: −001/2
 
[P\overline{4}2_{1}m] No. 113 (166)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{k}h\overline{l}]: (4) [k\overline{h}\overline{l}]:
(5) [\overline{h}k\overline{l}]: −110/2 (6) [h\overline{k}\overline{l}]: −110/2 (7) [\overline{k}\overline{h}l]: −110/2 (8) [khl]: −110/2
 
[P\overline{4}2_{1}c] No. 114 (167)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{k}h\overline{l}]: (4) [k\overline{h}\overline{l}]:
(5) [\overline{h}k\overline{l}]: −111/2 (6) [h\overline{k}\overline{l}]: −111/2 (7) [\overline{k}\overline{h}l]: −111/2 (8) [khl]: −111/2
 
[P\overline{4}m2] No. 115 (168)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{k}h\overline{l}]: (4) [k\overline{h}\overline{l}]:
(5) [h\overline{k}l]: (6) [\overline{h}kl]: (7) [kh\overline{l}]: (8) [\overline{k}\overline{h}\overline{l}]:
 
[P\overline{4}c2] No. 116 (169)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{k}h\overline{l}]: (4) [k\overline{h}\overline{l}]:
(5) [h\overline{k}l]: −001/2 (6) [\overline{h}kl]: −001/2 (7) [kh\overline{l}]: −001/2 (8) [\overline{k}\overline{h}\overline{l}]: −001/2
 
[P\overline{4}b2] No. 117 (170)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{k}h\overline{l}]: (4) [k\overline{h}\overline{l}]:
(5) [h\overline{k}l]: −110/2 (6) [\overline{h}kl]: −110/2 (7) [kh\overline{l}]: −110/2 (8) [\overline{k}\overline{h}\overline{l}]: −110/2
 
[P\overline{4}n2] No. 118 (171)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{k}h\overline{l}]: (4) [k\overline{h}\overline{l}]:
(5) [h\overline{k}l]: −111/2 (6) [\overline{h}kl]: −111/2 (7) [kh\overline{l}]: −111/2 (8) [\overline{k}\overline{h}\overline{l}]: −111/2
 
[I\overline{4}m2] No. 119 (172)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{k}h\overline{l}]: (4) [k\overline{h}\overline{l}]:
(5) [h\overline{k}l]: (6) [\overline{h}kl]: (7) [kh\overline{l}]: (8) [\overline{k}\overline{h}\overline{l}]:
 
[I\overline{4}c2] No. 120 (173)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{k}h\overline{l}]: (4) [k\overline{h}\overline{l}]:
(5) [h\overline{k}l]: −001/2 (6) [\overline{h}kl]: −001/2 (7) [kh\overline{l}]: −001/2 (8) [\overline{k}\overline{h}\overline{l}]: −001/2
 
[I\overline{4}2m] No. 121 (174)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{k}h\overline{l}]: (4) [k\overline{h}\overline{l}]:
(5) [\overline{h}k\overline{l}]: (6) [h\overline{k}\overline{l}]: (7) [\overline{k}\overline{h}l]: (8) [khl]:
 
[I\overline{4}2d] No. 122 (175)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{k}h\overline{l}]: (4) [k\overline{h}\overline{l}]:
(5) [\overline{h}k\overline{l}]: −203/4 (6) [h\overline{k}\overline{l}]: −203/4 (7) [\overline{k}\overline{h}l]: −021/4 (8) [khl]: −021/4

Point group: 4/mmm Tetragonal Laue group: 4/mmm
[P4/mmm] No. 123 (176)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: (4) [\overline{k}hl]:
(5) [\overline{h}k\overline{l}]: (6) [h\overline{k}\overline{l}]: (7) [kh\overline{l}]: (8) [\overline{k}\overline{h}\overline{l}]:
 
[P4/mcc] No. 124 (177)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: (4) [\overline{k}hl]:
(5) [\overline{h}k\overline{l}]: −001/2 (6) [h\overline{k}\overline{l}]: −001/2 (7) [kh\overline{l}]: −001/2 (8) [\overline{k}\overline{h}\overline{l}]: −001/2
 
[P4/nbm] Origin 1 No. 125 (178)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: (4) [\overline{k}hl]:
(5) [\overline{h}k\overline{l}]: (6) [h\overline{k}\overline{l}]: (7) [kh\overline{l}]: (8) [\overline{k}\overline{h}\overline{l}]:
(9) [\overline{h}\overline{k}\overline{l}]: −110/2 (10) [hk\overline{l}]: −110/2 (11) [\overline{k}h\overline{l}]: −110/2 (12) [k\overline{h}\overline{l}]: −110/2
(13) [h\overline{k}l]: −110/2 (14) [\overline{h}kl]: −110/2 (15) [\overline{k}\overline{h}l]: −110/2 (16) [khl]: −110/2
 
[P4/nbm] Origin 2 No. 125 (179)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −110/2 (3) [k\overline{h}l]: −100/2 (4) [\overline{k}hl]: −010/2
(5) [\overline{h}k\overline{l}]: −100/2 (6) [h\overline{k}\overline{l}]: −010/2 (7) [kh\overline{l}]: (8) [\overline{k}\overline{h}\overline{l}]: −110/2
 
[P4/nnc] Origin 1 No. 126 (180)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: (4) [\overline{k}hl]:
(5) [\overline{h}k\overline{l}]: (6) [h\overline{k}\overline{l}]: (7) [kh\overline{l}]: (8) [\overline{k}\overline{h}\overline{l}]:
(9) [\overline{h}\overline{k}\overline{l}]: −111/2 (10) [hk\overline{l}]: −111/2 (11) [\overline{k}h\overline{l}]: −111/2 (12) [k\overline{h}\overline{l}]: −111/2
(13) [h\overline{k}l]: −111/2 (14) [\overline{h}kl]: −111/2 (15) [\overline{k}\overline{h}l]: −111/2 (16) [khl]: −111/2
 
[P4/nnc] Origin 2 No. 126 (181)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −110/2 (3) [k\overline{h}l]: −100/2 (4) [\overline{k}hl]: −010/2
(5) [\overline{h}k\overline{l}]: −101/2 (6) [h\overline{k}\overline{l}]: −011/2 (7) [kh\overline{l}]: −001/2 (8) [\overline{k}\overline{h}\overline{l}]: −111/2
 
[P4/mbm] No. 127 (182)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: (4) [\overline{k}hl]:
(5) [\overline{h}k\overline{l}]: −110/2 (6) [h\overline{k}\overline{l}]: −110/2 (7) [kh\overline{l}]: −110/2 (8) [\overline{k}\overline{h}\overline{l}]: −110/2
 
[P4/mnc] No. 128 (183)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: (4) [\overline{k}hl]:
(5) [\overline{h}k\overline{l}]: −111/2 (6) [h\overline{k}\overline{l}]: −111/2 (7) [kh\overline{l}]: −111/2 (8) [\overline{k}\overline{h}\overline{l}]: −111/2
 
[P4/nmm] Origin 1 No. 129 (184)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: −110/2 (4) [\overline{k}hl]: −110/2
(5) [\overline{h}k\overline{l}]: −110/2 (6) [h\overline{k}\overline{l}]: −110/2 (7) [kh\overline{l}]: (8) [\overline{k}\overline{h}\overline{l}]:
(9) [\overline{h}\overline{k}\overline{l}]: −110/2 (10) [hk\overline{l}]: [-\!]110/2 (11) [\overline{k}h\overline{l}]: (12) [k\overline{h}\overline{l}]:
(13) [h\overline{k}l]: (14) [\overline{h}kl]: (15) [\overline{k}\overline{h}l]: −110/2 (16) [khl]: −110/2
 
[P4/nmm] Origin 2 No. 129 (185)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −110/2 (3) [k\overline{h}l]: −100/2 (4) [\overline{k}hl]: −010/2
(5) [\overline{h}k\overline{l}]: −010/2 (6) [h\overline{k}\overline{l}]: −100/2 (7) [kh\overline{l}]: −110/2 (8) [\overline{k}\overline{h}\overline{l}]:
 
[P4/ncc] Origin 1 No. 130 (186)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: −110/2 (4) [\overline{k}hl]: −110/2
(5) [\overline{h}k\overline{l}]: −111/2 (6) [h\overline{k}\overline{l}]: −111/2 (7) [kh\overline{l}]: −001/2 (8) [\overline{k}\overline{h}\overline{l}]: −001/2
(9) [\overline{h}\overline{k}\overline{l}]: −110/2 (10) [hk\overline{l}]: −110/2 (11) [\overline{k}h\overline{l}]: (12) [k\overline{h}\overline{l}]:
(13) [h\overline{k}l]: −001/2 (14) [\overline{h}kl]: −001/2 (15) [\overline{k}\overline{h}l]: −111/2 (16) [khl]: −111/2
 
[P4/ncc] Origin 2 No. 130 (187)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −110/2 (3) [k\overline{h}l]: −100/2 (4) [\overline{k}hl]: −010/2
(5) [\overline{h}k\overline{l}]: −011/2 (6) [h\overline{k}\overline{l}]: −101/2 (7) [kh\overline{l}]: −111/2 (8) [\overline{k}\overline{h}\overline{l}]: −001/2
 
[P4_{2}/mmc] No. 131 (188)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: −001/2 (4) [\overline{k}hl]: −001/2
(5) [\overline{h}k\overline{l}]: (6) [h\overline{k}\overline{l}]: (7) [kh\overline{l}]: −001/2 (8) [\overline{k}\overline{h}\overline{l}]: −001/2
 
[P4_{2}/mcm] No. 132 (189)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: −001/2 (4) [\overline{k}hl]: −001/2
(5) [\overline{h}k\overline{l}]: −001/2 (6) [h\overline{k}\overline{l}]: −001/2 (7) [kh\overline{l}]: (8) [\overline{k}\overline{h}\overline{l}]:
 
[P4_{2}/nbc] Origin 1 No. 133 (190)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: −111/2 (4) [\overline{k}hl]: −111/2
(5) [\overline{h}k\overline{l}]: −001/2 (6) [h\overline{k}\overline{l}]: −001/2 (7) [kh\overline{l}]: −110/2 (8) [\overline{k}\overline{h}\overline{l}]: −110/2
(9) [\overline{h}\overline{k}\overline{l}]: −111/2 (10) [hk\overline{l}]: [-\!]111/2 (11) [\overline{k}h\overline{l}]: (12) [k\overline{h}\overline{l}]:
(13) [h\overline{k}l]: −110/2 (14) [\overline{h}kl]: −110/2 (15) [\overline{k}\overline{h}l]: −001/2 (16) [khl]: −001/2
 
[P4_{2}/nbc] Origin 2 No. 133 (191)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −110/2 (3) [k\overline{h}l]: −101/2 (4) [\overline{k}hl]: −011/2
(5) [\overline{h}k\overline{l}]: −100/2 (6) [h\overline{k}\overline{l}]: −010/2 (7) [kh\overline{l}]: −001/2 (8) [\overline{k}\overline{h}\overline{l}]: −111/2
 
[P4_{2}/nnm] Origin 1 No. 134 (192)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: −111/2 (4) [\overline{k}hl]: −111/2
(5) [\overline{h}k\overline{l}]: (6) [h\overline{k}\overline{l}]: (7) [kh\overline{l}]: −111/2 (8) [\overline{k}\overline{h}\overline{l}]: −111/2
(9) [\overline{h}\overline{k}\overline{l}]: −111/2 (10) [hk\overline{l}]: −111/2 (11) [\overline{k}h\overline{l}]: (12) [k\overline{h}\overline{l}]:
(13) [h\overline{k}l]: −111/2 (14) [\overline{h}kl]: −111/2 (15) [\overline{k}\overline{h}l]: (16) [khl]:
 
[P4_{2}/nnm] Origin 2 No. 134 (193)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −110/2 (3) [k\overline{h}l]: −101/2 (4) [\overline{k}hl]: −011/2
(5) [\overline{h}k\overline{l}]: −101/2 (6) [h\overline{k}\overline{l}]: −011/2 (7) [kh\overline{l}]: (8) [\overline{k}\overline{h}\overline{l}]: −110/2
 
[P4_{2}/mbc] No. 135 (194)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: −001/2 (4) [\overline{k}hl]: −001/2
(5) [\overline{h}k\overline{l}]: −110/2 (6) [h\overline{k}\overline{l}]: −110/2 (7) [kh\overline{l}]: −111/2 (8) [\overline{k}\overline{h}\overline{l}]: −111/2
 
[P4_{2}/mnm] No. 136 (195)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: −111/2 (4) [\overline{k}hl]: −111/2
(5) [\overline{h}k\overline{l}]: −111/2 (6) [h\overline{k}\overline{l}]: −111/2 (7) [kh\overline{l}]: (8) [\overline{k}\overline{h}\overline{l}]:
 
[P4_{2}/nmc] Origin 1 No. 137 (196)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: −111/2 (4) [\overline{k}hl]: −111/2
(5) [\overline{h}k\overline{l}]: −111/2 (6) [h\overline{k}\overline{l}]: −111/2 (7) [kh\overline{l}]: (8) [\overline{k}\overline{h}\overline{l}]:
(9) [\overline{h}\overline{k}\overline{l}]: −111/2 (10) [hk\overline{l}]: −111/2 (11) [\overline{k}h\overline{l}]: (12) [k\overline{h}\overline{l}]:
(13) [h\overline{k}l]: (14) [\overline{h}kl]: (15) [\overline{k}\overline{h}l]: −111/2 (16) [khl]: −111/2
 
[P4_{2}/nmc] Origin 2 No. 137 (197)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −110/2 (3) [k\overline{h}l]: −101/2 (4) [\overline{k}hl]: −011/2
(5) [\overline{h}k\overline{l}]: −010/2 (6) [h\overline{k}\overline{l}]: −100/2 (7) [kh\overline{l}]: −111/2 (8) [\overline{k}\overline{h}\overline{l}]: −001/2
 
[P4_{2}/ncm] Origin 1 No. 138 (198)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: −111/2 (4) [\overline{k}hl]: −111/2
(5) [\overline{h}k\overline{l}]: −110/2 (6) [h\overline{k}\overline{l}]: −110/2 (7) [kh\overline{l}]: −001/2 (8) [\overline{k}\overline{h}\overline{l}]: −001/2
(9) [\overline{h}\overline{k}\overline{l}]: −111/2 (10) [hk\overline{l}]: [-\!]111/2 (11) [\overline{k}h\overline{l}]: (12) [k\overline{h}\overline{l}]:
(13) [h\overline{k}l]: −001/2 (14) [\overline{h}kl]: −001/2 (15) [\overline{k}\overline{h}l]: −110/2 (16) [khl]: −110/2
 
[P4_{2}/ncm] Origin 2 No. 138 (199)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −110/2 (3) [k\overline{h}l]: −101/2 (4) [\overline{k}hl]: −011/2
(5) [\overline{h}k\overline{l}]: −011/2 (6) [h\overline{k}\overline{l}]: −101/2 (7) [kh\overline{l}]: −110/2 (8) [\overline{k}\overline{h}\overline{l}]:
 
[I4/mmm] No. 139 (200)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: (4) [\overline{k}hl]:
(5) [\overline{h}k\overline{l}]: (6) [h\overline{k}\overline{l}]: (7) [kh\overline{l}]: (8) [\overline{k}\overline{h}\overline{l}]:
 
[I4/mcm] No. 140 (201)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [k\overline{h}l]: (4) [\overline{k}hl]:
(5) [\overline{h}k\overline{l}]: −001/2 (6) [h\overline{k}\overline{l}]: −001/2 (7) [kh\overline{l}]: −001/2 (8) [\overline{k}\overline{h}\overline{l}]: −001/2
 
[I4_{1}/amd] Origin 1 No. 141 (202)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −111/2 (3) [k\overline{h}l]: −021/4 (4) [\overline{k}hl]: −203/4
(5) [\overline{h}k\overline{l}]: −203/4 (6) [h\overline{k}\overline{l}]: −021/4 (7) [kh\overline{l}]: −111/2 (8) [\overline{k}\overline{h}\overline{l}]:
(9) [\overline{h}\overline{k}\overline{l}]: −021/4 (10) [hk\overline{l}]: −203/4 (11) [\overline{k}h\overline{l}]: (12) [k\overline{h}\overline{l}]: −111/2
(13) [h\overline{k}l]: −111/2 (14) [\overline{h}kl]: (15) [\overline{k}\overline{h}l]: −203/4 (16) [khl]: −021/4
 
[I4_{1}/amd] Origin 2 No. 141 (203)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −101/2 (3) [k\overline{h}l]: −131/4 (4) [\overline{k}hl]: −113/4
(5) [\overline{h}k\overline{l}]: −101/2 (6) [h\overline{k}\overline{l}]: (7) [kh\overline{l}]: −131/4 (8) [\overline{k}\overline{h}\overline{l}]: −113/4
 
[I4_{1}/acd] Origin 1 No. 142 (204)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −111/2 (3) [k\overline{h}l]: −021/4 (4) [\overline{k}hl]: −203/4
(5) [\overline{h}k\overline{l}]: −201/4 (6) [h\overline{k}\overline{l}]: −023/4 (7) [kh\overline{l}]: −110/2 (8) [\overline{k}\overline{h}\overline{l}]: −001/2
(9) [\overline{h}\overline{k}\overline{l}]: −021/4 (10) [hk\overline{l}]: [-\!]203/4 (11) [\overline{k}h\overline{l}]: (12) [k\overline{h}\overline{l}]: −111/2
(13) [h\overline{k}l]: −110/2 (14) [\overline{h}kl]: −001/2 (15) [\overline{k}\overline{h}l]: −201/4 (16) [khl]: −023/4
 
[I4_{1}/acd] Origin 2 No. 142 (205)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −101/2 (3) [k\overline{h}l]: −131/4 (4) [\overline{k}hl]: −113/4
(5) [\overline{h}k\overline{l}]: −100/2 (6) [h\overline{k}\overline{l}]: −001/2 (7) [kh\overline{l}]: −133/4 (8) [\overline{k}\overline{h}\overline{l}]: −111/4

Point group: 3 Trigonal Laue group: [\bf{{\overline{3}}}]
[P3] No. 143 (206)
(1) [hkl]: (2) [kil]: (3) [ihl]:
 
[P3_{1}] No. 144 (207)
(1) [hkl]: (2) [kil]: −001/3 (3) [ihl]: −002/3
 
[P3_{2}] No. 145 (208)
(1) [hkl]: (2) [kil]: −002/3 (3) [ihl]: −001/3
 
[R3] (hexagonal axes) No. 146 (209)
(1) [hkl]: (2) [kil]: (3) [ihl]:
 
[R3] (rhombohedral axes) No. 146 (210)
(1) [hkl]: (2) [klh]: (3) [lhk]:

Point group: [\bf{{\overline{3}}}] Trigonal Laue group: [\bf{{\overline{3}}}]
[P\overline{3}] No. 147 (211)
(1) [hkl]: (2) [kil]: (3) [ihl]:
 
[R\overline{3}] (hexagonal axes) No. 148 (212)
(1) [hkl]: (2) [kil]: (3) [ihl]:
 
[R\overline{3}] (rhombohedral axes) No. 148 (213)
(1) [hkl]: (2) [klh]: (3) [lhk]:

Point group: 32 Trigonal Laue group: [\bf{{\overline{3}}}]m
[P312] No. 149 (214)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [\overline{k}\overline{h}\overline{l}]: (5) [\overline{h}\overline{\vphantom{l}i}\overline{l}]: (6) [\overline{\vphantom{l}i}\overline{k}\overline{l}]:
 
[P321] No. 150 (215)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [kh\overline{l}]: (5) [hi\overline{l}]: (6) [ik\overline{l}]:
 
[P3_{1}12] No. 151 (216)
(1) [hkl]: (2) [kil]: −001/3 (3) [ihl]: −002/3
(4) [\overline{k}\overline{h}\overline{l}]: −002/3 (5) [\overline{h}\overline{\vphantom{l}i}\overline{l}]: −001/3 (6) [\overline{\vphantom{l}i}\overline{k}\overline{l}]:
 
[P3_{1}21] No. 152 (217)
(1) [hkl]: (2) [kil]: −001/3 (3) [ihl]: −002/3
(4) [kh\overline{l}]: (5) [hi\overline{l}]: −002/3 (6) [ik\overline{l}]: −001/3
 
[P3_{2}12] No. 153 (218)
(1) [hkl]: (2) [kil]: −002/3 (3) [ihl]: −001/3
(4) [\overline{k}\overline{h}\overline{l}]: −001/3 (5) [\overline{h}\overline{\vphantom{l}i}\overline{l}]: −002/3 (6) [\overline{\vphantom{l}i}\overline{k}\overline{l}]:
 
[P3_{2}21] No. 154 (219)
(1) [hkl]: (2) [kil]: −002/3 (3) [ihl]: −001/3
(4) [kh\overline{l}]: (5) [hi\overline{l}]: −001/3 (6) [ik\overline{l}]: −002/3
 
[R32] (hexagonal axes) No. 155 (220)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [kh\overline{l}]: (5) [hi\overline{l}]: (6) [ik\overline{l}]:
 
[R32] (rhombohedral axes) No. 155 (221)
(1) [hkl]: (2) [klh]: (3) [lhk]:
(4) [\overline{k}\overline{h}\overline{l}]: (5) [\overline{h}\overline{l}\overline{k}]: (6) [\overline{l}\overline{k}\overline{h}]:

Point group: 3m Trigonal Laue group: [\bf{{\overline{3}}}]m
[P3m1] No. 156 (222)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [\overline{k}\overline{h}l]: (5) [\overline{h}\overline{\vphantom{l}i}l]: (6) [\overline{\vphantom{l}i}\overline{k}l]:
 
[P31m] No. 157 (223)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [khl]: (5) [hil]: (6) [ikl]:
 
[P3c1] No. 158 (224)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [\overline{k}\overline{h}l]: −001/2 (5) [\overline{h}\overline{\vphantom{l}i}l]: −001/2 (6) [\overline{\vphantom{l}i}\overline{k}l]: −001/2
 
[P31c] No. 159 (225)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [khl]: −001/2 (5) [hil]: −001/2 (6) [ikl]: −001/2
 
[R3m] (hexagonal axes) No. 160 (226)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [\overline{k}\overline{h}l]: (5) [\overline{h}\overline{\vphantom{l}i}l]: (6) [\overline{\vphantom{l}i}\overline{k}l]:
 
[R3m] (rhombohedral axes) No. 160 (227)
(1) [hkl]: (2) [klh]: (3) [lhk]:
(4) [khl]: (5) [hlk]: (6) [lkh]:
 
[R3c] (hexagonal axes) No. 161 (228)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [\overline{k}\overline{h}l]: −001/2 (5) [\overline{h}\overline{\vphantom{l}i}l]: −001/2 (6) [\overline{\vphantom{l}i}\overline{k}l]: −001/2
 
[R3c] (rhombohedral axes) No. 161 (229)
(1) [hkl]: (2) [klh]: (3) [lhk]:
(4) [khl]: −111/2 (5) [hlk]: −111/2 (6) [lkh]: −111/2

Point group: [\bf{{\overline{3}}}]m Trigonal Laue group: [\bf{{\overline{3}}}]m
[P\overline{3}1m] No. 162 (230)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [\overline{k}\overline{h}\overline{l}]: (5) [\overline{h}\overline{\vphantom{l}i}\overline{l}]: (6) [\overline{\vphantom{l}i}\overline{k}\overline{l}]:
 
[P\overline{3}1c] No. 163 (231)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [\overline{k}\overline{h}\overline{l}]: −001/2 (5) [\overline{h}\overline{\vphantom{l}i}\overline{l}]: −001/2 (6) [\overline{\vphantom{l}i}\overline{k}\overline{l}]: −001/2
 
[P\overline{3}m1] No. 164 (232)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [kh\overline{l}]: (5) [hi\overline{l}]: (6) [ik\overline{l}]:
 
[P\overline{3}c1] No. 165 (233)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [kh\overline{l}]: −001/2 (5) [hi\overline{l}]: −001/2 (6) [ik\overline{l}]: −001/2
 
[R\overline{3}m] (hexagonal axes) No. 166 (234)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [kh\overline{l}]: (5) [hi\overline{l}]: (6) [ik\overline{l}]:
 
[R\overline{3}m] (rhombohedral axes) No. 166 (235)
(1) [hkl]: (2) [klh]: (3) [lhk]:
(4) [\overline{k}\overline{h}\overline{l}]: (5) [\overline{h}\overline{l}\overline{k}]: (6) [\overline{l}\overline{k}\overline{h}]:
 
[R\overline{3}c] (hexagonal axes) No. 167 (236)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [kh\overline{l}]: −001/2 (5) [hi\overline{l}]: −001/2 (6) [ik\overline{l}]: −001/2
 
[R\overline{3}c] (rhombohedral axes) No. 168 (237)
(1) [hkl]: (2) [klh]: (3) [lhk]:
(4) [\overline{k}\overline{h}\overline{l}]: −111/2 (5) [\overline{h}\overline{l}\overline{k}]: −111/2 (6) [\overline{l}\overline{k}\overline{h}]: −111/2

Point group: 6 Hexagonal Laue group: 6/m
[P6] No. 168 (238)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [\overline{h}\overline{k}l]: (5) [\overline{k}\overline{\vphantom{l}i}l]: (6) [\overline{\vphantom{l}i}\overline{h}l]:
 
[P6_{1}] No. 169 (239)
(1) [hkl]: (2) [kil]: −001/3 (3) [ihl]: −002/3
(4) [\overline{h}\overline{k}l]: −001/2 (5) [\overline{k}\overline{\vphantom{l}i}l]: −005/6 (6) [\overline{\vphantom{l}i}\overline{h}l]: −001/6
 
[P6_{5}] No. 170 (240)
(1) [hkl]: (2) [kil]: −002/3 (3) [ihl]: −001/3
(4) [\overline{h}\overline{k}l]: −001/2 (5) [\overline{k}\overline{\vphantom{l}i}l]: −001/6 (6) [\overline{\vphantom{l}i}\overline{h}l]: −005/6
 
[P6_{2}] No. 171 (241)
(1) [hkl]: (2) [kil]: −002/3 (3) [ihl]: −001/3
(4) [\overline{h}\overline{k}l]: (5) [\overline{k}\overline{\vphantom{l}i}l]: −002/3 (6) [\overline{\vphantom{l}i}\overline{h}l]: −001/3
 
[P6_{4}] No. 172 (242)
(1) [hkl]: (2) [kil]: −001/3 (3) [ihl]: −002/3
(4) [\overline{h}\overline{k}l]: (5) [\overline{k}\overline{\vphantom{l}i}l]: −001/3 (6) [\overline{\vphantom{l}i}\overline{h}l]: −002/3
 
[P6_{3}] No. 173 (243)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [\overline{h}\overline{k}l]: −001/2 (5) [\overline{k}\overline{\vphantom{l}i}l]: −001/2 (6) [\overline{\vphantom{l}i}\overline{h}l]: −001/2

Point group: [\bf{{\overline{6}}}] Hexagonal Laue group: 6/m
[P\overline{6}] No. 174 (244)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [hk\overline{l}]: (5) [ki\overline{l}]: (6) [ih\overline{l}]:

Point group: 6/m Hexagonal Laue group: 6/m
[P6/m] No. 175 (245)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [\overline{h}\overline{k}l]: (5) [\overline{k}\overline{\vphantom{l}i}l]: (6) [\overline{\vphantom{l}i}\overline{h}l]:
 
[P6_{3}/m] No. 176 (246)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [\overline{h}\overline{k}l]: −001/2 (5) [\overline{k}\overline{\vphantom{l}i}l]: −001/2 (6) [\overline{\vphantom{l}i}\overline{h}l]: −001/2

Point group: 622 Hexagonal Laue group: 6/mmm
[P622] No. 177 (247)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [\overline{h}\overline{k}l]: (5) [\overline{k}\overline{\vphantom{l}i}l]: (6) [\overline{\vphantom{l}i}\overline{h}l]:
(7) [kh\overline{l}]: (8) [hi\overline{l}]: (9) [ik\overline{l}]:
(10) [\overline{k}\overline{h}\overline{l}]: (11) [\overline{h}\overline{\vphantom{l}i}\overline{l}]: (12) [\overline{\vphantom{l}i}\overline{k}\overline{l}]:
 
[P6_{1}22] No. 178 (248)
(1) [hkl]: (2) [kil]: −001/3 (3) [ihl]: −002/3
(4) [\overline{h}\overline{k}l]: −001/2 (5) [\overline{k}\overline{\vphantom{l}i}l]: −005/6 (6) [\overline{\vphantom{l}i}\overline{h}l]: −001/6
(7) [kh\overline{l}]: −001/3 (8) [hi\overline{l}]: (9) [ik\overline{l}]: −002/3
(10) [\overline{k}\overline{h}\overline{l}]: −005/6 (11) [\overline{h}\overline{\vphantom{l}i}\overline{l}]: −001/2 (12) [\overline{\vphantom{l}i}\overline{k}\overline{l}]: −001/6
 
[P6_{5}22] No. 179 (249)
(1) [hkl]: (2) [kil]: −002/3 (3) [ihl]: −001/3
(4) [\overline{h}\overline{k}l]: −001/2 (5) [\overline{k}\overline{\vphantom{l}i}l]: −001/6 (6) [\overline{\vphantom{l}i}\overline{h}l]: −005/6
(7) [kh\overline{l}]: −002/3 (8) [hi\overline{l}]: (9) [ik\overline{l}]: −001/3
(10) [\overline{k}\overline{h}\overline{l}]: −001/6 (11) [\overline{h}\overline{\vphantom{l}i}\overline{l}]: −001/2 (12) [\overline{\vphantom{l}i}\overline{k}\overline{l}]: −005/6
 
[P6_{2}22] No. 180 (250)
(1) [hkl]: (2) [kil]: −002/3 (3) [ihl]: −001/3
(4) [\overline{h}\overline{k}l]: (5) [\overline{k}\overline{\vphantom{l}i}l]: −002/3 (6) [\overline{\vphantom{l}i}\overline{h}l]: −001/3
(7) [kh\overline{l}]: −002/3 (8) [hi\overline{l}]: (9) [ik\overline{l}]: −001/3
(10) [\overline{k}\overline{h}\overline{l}]: −002/3 (11) [\overline{h}\overline{\vphantom{l}i}\overline{l}]: (12) [\overline{\vphantom{l}i}\overline{k}\overline{l}]: −001/3
 
[P6_{4}22] No. 181 (251)
(1) [hkl]: (2) [kil]: −001/3 (3) [ihl]: −002/3
(4) [\overline{h}\overline{k}l]: (5) [\overline{k}\overline{\vphantom{l}i}l]: −001/3 (6) [\overline{\vphantom{l}i}\overline{h}l]: −002/3
(7) [kh\overline{l}]: −001/3 (8) [hi\overline{l}]: (9) [ik\overline{l}]: −002/3
(10) [\overline{k}\overline{h}\overline{l}]: −001/3 (11) [\overline{h}\overline{\vphantom{l}i}\overline{l}]: (12) [\overline{\vphantom{l}i}\overline{k}\overline{l}]: −002/3
 
[P6_{3}22] No. 182 (252)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [\overline{h}\overline{k}l]: −001/2 (5) [\overline{k}\overline{\vphantom{l}i}l]: −001/2 (6) [\overline{\vphantom{l}i}\overline{h}l]: −001/2
(7) [kh\overline{l}]: (8) [hi\overline{l}]: (9) [ik\overline{l}]:
(10) [\overline{k}\overline{h}\overline{l}]: −001/2 (11) [\overline{h}\overline{\vphantom{l}i}\overline{l}]: −001/2 (12) [\overline{\vphantom{l}i}\overline{k}\overline{l}]: −001/2

Point group: 6mm Hexagonal Laue group: 6/mmm
[P6mm] No. 183 (253)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [\overline{h}\overline{k}l]: (5) [\overline{k}\overline{\vphantom{l}i}l]: (6) [\overline{\vphantom{l}i}\overline{h}l]:
(7) [\overline{k}\overline{h}l]: (8) [\overline{h}\overline{\vphantom{l}i}l]: (9) [\overline{\vphantom{l}i}\overline{k}l]:
(10) [khl]: (11) [hil]: (12) [ikl]:
 
[P6cc] No. 184 (254)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [\overline{h}\overline{k}l]: (5) [\overline{k}\overline{\vphantom{l}i}l]: (6) [\overline{\vphantom{l}i}\overline{h}l]:
(7) [\overline{k}\overline{h}l]: −001/2 (8) [\overline{h}\overline{\vphantom{l}i}l]: −001/2 (9) [\overline{\vphantom{l}i}\overline{k}l]: −001/2
(10) [khl]: −001/2 (11) [hil]: −001/2 (12) [ikl]: −001/2
 
[P6_{3}cm] No. 185 (255)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [\overline{h}\overline{k}l]: −001/2 (5) [\overline{k}\overline{\vphantom{l}i}l]: −001/2 (6) [\overline{\vphantom{l}i}\overline{h}l]: −001/2
(7) [\overline{k}\overline{h}l]: −001/2 (8) [\overline{h}\overline{\vphantom{l}i}l]: −001/2 (9) [\overline{\vphantom{l}i}\overline{k}l]: −001/2
(10) [khl]: (11) [hil]: (12) [ikl]:
 
[P6_{3}mc] No. 186 (256)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [\overline{h}\overline{k}l]: −001/2 (5) [\overline{k}\overline{\vphantom{l}i}l]: −001/2 (6) [\overline{\vphantom{l}i}\overline{h}l]: −001/2
(7) [\overline{k}\overline{h}l]: (8) [\overline{h}\overline{\vphantom{l}i}l]: (9) [\overline{\vphantom{l}i}\overline{k}l]:
(10) [khl]: −001/2 (11) [hil]: −001/2 (12) [ikl]: −001/2

Point group: [\bf{{\overline{6}}}]m2 Hexagonal Laue group: 6/mmm
[P\overline{6}m2] No. 187 (257)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [hk\overline{l}]: (5) [ki\overline{l}]: (6) [ih\overline{l}]:
(7) [\overline{k}\overline{h}l]: (8) [\overline{h}\overline{\vphantom{l}i}l]: (9) [\overline{\vphantom{l}i}\overline{k}l]:
(10) [\overline{k}\overline{h}\overline{l}]: (11) [\overline{h}\overline{\vphantom{l}i}\overline{l}]: (12) [\overline{\vphantom{l}i}\overline{k}\overline{l}]:
 
[P\overline{6}c2] No. 188 (258)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [hk\overline{l}]: −001/2 (5) [ki\overline{l}]: −001/2 (6) [ih\overline{l}]: −001/2
(7) [\overline{k}\overline{h}l]: −001/2 (8) [\overline{h}\overline{\vphantom{l}i}l]: −001/2 (9) [\overline{\vphantom{l}i}\overline{k}l]: −001/2
(10) [\overline{k}\overline{h}\overline{l}]: (11) [\overline{h}\overline{\vphantom{l}i}\overline{l}]: (12) [\overline{\vphantom{l}i}\overline{k}\overline{l}]:
 
[P\overline{6}2m] No. 189 (259)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [hk\overline{l}]: (5) [ki\overline{l}]: (6) [ih\overline{l}]:
(7) [kh\overline{l}]: (8) [hi\overline{l}]: (9) [ik\overline{l}]:
(10) [khl]: (11) [hil]: (12) [ikl]:
 
[P\overline{6}2c] No. 190 (260)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [hk\overline{l}]: −001/2 (5) [ki\overline{l}]: −001/2 (6) [ih\overline{l}]: −001/2
(7) [kh\overline{l}]: (8) [hi\overline{l}]: (9) [ik\overline{l}]:
(10) [khl]: −001/2 (11) [hil]: −001/2 (12) [ikl]: −001/2

Point group: 6/mmm Hexagonal Laue group: 6/mmm
[P6/mmm] No. 191 (261)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [\overline{h}\overline{k}l]: (5) [\overline{k}\overline{\vphantom{l}i}l]: (6) [\overline{\vphantom{l}i}\overline{h}l]:
(7) [kh\overline{l}]: (8) [hi\overline{l}]: (9) [ik\overline{l}]:
(10) [\overline{k}\overline{h}\overline{l}]: (11) [\overline{h}\overline{\vphantom{l}i}\overline{l}]: (12) [\overline{\vphantom{l}i}\overline{k}\overline{l}]:
 
[P6/mcc] No. 192 (262)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [\overline{h}\overline{k}l]: (5) [\overline{k}\overline{\vphantom{l}i}l]: (6) [\overline{\vphantom{l}i}\overline{h}l]:
(7) [kh\overline{l}]: −001/2 (8) [hi\overline{l}]: −001/2 (9) [ik\overline{l}]: −001/2
(10) [\overline{k}\overline{h}\overline{l}]: −001/2 (11) [\overline{h}\overline{\vphantom{l}i}\overline{l}]: −001/2 (12) [\overline{\vphantom{l}i}\overline{k}\overline{l}]: −001/2
 
[P6_{3}/mcm] No. 193 (263)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [\overline{h}\overline{k}l]: −001/2 (5) [\overline{k}\overline{\vphantom{l}i}l]: −001/2 (6) [\overline{\vphantom{l}i}\overline{h}l]: −001/2
(7) [kh\overline{l}]: −001/2 (8) [hi\overline{l}]: −001/2 (9) [ik\overline{l}]: −001/2
(10) [\overline{k}\overline{h}\overline{l}]: (11) [\overline{h}\overline{\vphantom{l}i}\overline{l}]: (12) [\overline{\vphantom{l}i}\overline{k}\overline{l}]:
 
[P6_{3}/mmc] No. 194 (264)
(1) [hkl]: (2) [kil]: (3) [ihl]:
(4) [\overline{h}\overline{k}l]: −001/2 (5) [\overline{k}\overline{\vphantom{l}i}l]: −001/2 (6) [\overline{\vphantom{l}i}\overline{h}l]: −001/2
(7) [kh\overline{l}]: (8) [hi\overline{l}]: (9) [ik\overline{l}]:
(10) [\overline{k}\overline{h}\overline{l}]: −001/2 (11) [\overline{h}\overline{\vphantom{l}i}\overline{l}]: −001/2 (12) [\overline{\vphantom{l}i}\overline{k}\overline{l}]: −001/2

Point group: 23 Cubic Laue group: m[\bf{{\overline{3}}}]
[P23] No. 195 (265)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
(5) [klh]: (6) [\overline{k}\overline{l}h]: (7) [\overline{k}l\overline{h}]: (8) [k\overline{l}\overline{h}]:
(9) [lhk]: (10) [\overline{l}\overline{h}k]: (11) [\overline{l}h\overline{k}]: (12) [l\overline{h}\overline{k}]:
 
[F23] No. 196 (266)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
(5) [klh]: (6) [\overline{k}\overline{l}h]: (7) [\overline{k}l\overline{h}]: (8) [k\overline{l}\overline{h}]:
(9) [lhk]: (10) [\overline{l}\overline{h}k]: (11) [\overline{l}h\overline{k}]: (12) [l\overline{h}\overline{k}]:
 
[I23] No. 197 (267)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
(5) [klh]: (6) [\overline{k}\overline{l}h]: (7) [\overline{k}l\overline{h}]: (8) [k\overline{l}\overline{h}]:
(9) [lhk]: (10) [\overline{l}\overline{h}k]: (11) [\overline{l}h\overline{k}]: (12) [l\overline{h}\overline{k}]:
 
[P2_{1}3] No. 198 (268)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −101/2 (3) [\overline{h}k\overline{l}]: −011/2 (4) [h\overline{k}\overline{l}]: −110/2
(5) [klh]: (6) [\overline{k}\overline{l}h]: −110/2 (7) [\overline{k}l\overline{h}]: −101/2 (8) [k\overline{l}\overline{h}]: −011/2
(9) [lhk]: (10) [\overline{l}\overline{h}k]: −011/2 (11) [\overline{l}h\overline{k}]: −110/2 (12) [l\overline{h}\overline{k}]: −101/2
 
[I2_{1}3] No. 199 (269)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −101/2 (3) [\overline{h}k\overline{l}]: −011/2 (4) [h\overline{k}\overline{l}]: −110/2
(5) [klh]: (6) [\overline{k}\overline{l}h]: −110/2 (7) [\overline{k}l\overline{h}]: −101/2 (8) [k\overline{l}\overline{h}]: −011/2
(9) [lhk]: (10) [\overline{l}\overline{h}k]: −011/2 (11) [\overline{l}h\overline{k}]: −110/2 (12) [l\overline{h}\overline{k}]: −101/2

Point group: m[\bf{{\overline{3}}}] Cubic Laue group: m[\bf{{\overline{3}}}]
[Pm\overline{3}] No. 200 (270)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
(5) [klh]: (6) [\overline{k}\overline{l}h]: (7) [\overline{k}l\overline{h}]: (8) [k\overline{l}\overline{h}]:
(9) [lhk]: (10) [\overline{l}\overline{h}k]: (11) [\overline{l}h\overline{k}]: (12) [l\overline{h}\overline{k}]:
 
[Pn\overline{3}] Origin 1 No. 201 (271)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
(5) [klh]: (6) [\overline{k}\overline{l}h]: (7) [\overline{k}l\overline{h}]: (8) [k\overline{l}\overline{h}]:
(9) [lhk]: (10) [\overline{l}\overline{h}k]: (11) [\overline{l}h\overline{k}]: (12) [l\overline{h}\overline{k}]:
(13) [\overline{h}\overline{k}\overline{l}]: −111/2 (14) [hk\overline{l}]: −111/2 (15) [h\overline{k}l]: −111/2 (16) [\overline{h}kl]: −111/2
(17) [\overline{k}\overline{l}\overline{h}]: −111/2 (18) [kl\overline{h}]: −111/2 (19) [k\overline{l}h]: −111/2 (20) [\overline{k}lh]: −111/2
(21) [\overline{l}\overline{h}\overline{k}]: −111/2 (22) [lh\overline{k}]: −111/2 (23) [l\overline{h}k]: −111/2 (24) [\overline{l}hk]: −111/2
 
[Pn\overline{3}] Origin 2 No. 201 (272)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −110/2 (3) [\overline{h}k\overline{l}]: −101/2 (4) [h\overline{k}\overline{l}]: −011/2
(5) [klh]: (6) [\overline{k}\overline{l}h]: −011/2 (7) [\overline{k}l\overline{h}]: −110/2 (8) [k\overline{l}\overline{h}]: −101/2
(9) [lhk]: (10) [\overline{l}\overline{h}k]: −101/2 (11) [\overline{l}h\overline{k}]: −011/2 (12) [l\overline{h}\overline{k}]: −110/2
 
[Fm\overline{3}] No. 202 (273)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
(5) [klh]: (6) [\overline{k}\overline{l}h]: (7) [\overline{k}l\overline{h}]: (8) [k\overline{l}\overline{h}]:
(9) [lhk]: (10) [\overline{l}\overline{h}k]: (11) [\overline{l}h\overline{k}]: (12) [l\overline{h}\overline{k}]:
 
[Fd\overline{3}] Origin 1 No. 203 (274)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
(5) [klh]: (6) [\overline{k}\overline{l}h]: (7) [\overline{k}l\overline{h}]: (8) [k\overline{l}\overline{h}]:
(9) [lhk]: (10) [\overline{l}\overline{h}k]: (11) [\overline{l}h\overline{k}]: (12) [l\overline{h}\overline{k}]:
(13) [\overline{h}\overline{k}\overline{l}]: −111/4 (14) [hk\overline{l}]: −111/4 (15) [h\overline{k}l]: −111/4 (16) [\overline{h}kl]: −111/4
(17) [\overline{k}\overline{l}\overline{h}]: −111/4 (18) [kl\overline{h}]: −111/4 (19) [k\overline{l}h]: −111/4 (20) [\overline{k}lh]: −111/4
(21) [\overline{l}\overline{h}\overline{k}]: −111/4 (22) [lh\overline{k}]: −111/4 (23) [l\overline{h}k]: −111/4 (24) [\overline{l}hk]: −111/4
 
[Fd\overline{3}] Origin 2 No. 203 (275)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −110/4 (3) [\overline{h}k\overline{l}]: −101/4 (4) [h\overline{k}\overline{l}]: −011/4
(5) [klh]: (6) [\overline{k}\overline{l}h]: −011/4 (7) [\overline{k}l\overline{h}]: −110/4 (8) [k\overline{l}\overline{h}]: −101/4
(9) [lhk]: (10) [\overline{l}\overline{h}k]: −101/4 (11) [\overline{l}h\overline{k}]: −011/4 (12) [l\overline{h}\overline{k}]: −110/4
 
[Im\overline{3}] No. 204 (276)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
(5) [klh]: (6) [\overline{k}\overline{l}h]: (7) [\overline{k}l\overline{h}]: (8) [k\overline{l}\overline{h}]:
(9) [lhk]: (10) [\overline{l}\overline{h}k]: (11) [\overline{l}h\overline{k}]: (12) [l\overline{h}\overline{k}]:
 
[Pa\overline{3}] No. 205 (277)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −101/2 (3) [\overline{h}k\overline{l}]: −011/2 (4) [h\overline{k}\overline{l}]: −110/2
(5) [klh]: (6) [\overline{k}\overline{l}h]: −110/2 (7) [\overline{k}l\overline{h}]: −101/2 (8) [k\overline{l}\overline{h}]: −011/2
(9) [lhk]: (10) [\overline{l}\overline{h}k]: −011/2 (11) [\overline{l}h\overline{k}]: −110/2 (12) [l\overline{h}\overline{k}]: −101/2
 
[Ia\overline{3}] No. 206 (278)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −101/2 (3) [\overline{h}k\overline{l}]: −011/2 (4) [h\overline{k}\overline{l}]: −110/2
(5) [klh]: (6) [\overline{k}\overline{l}h]: −110/2 (7) [\overline{k}l\overline{h}]: −101/2 (8) [k\overline{l}\overline{h}]: −011/2
(9) [lhk]: (10) [\overline{l}\overline{h}k]: −011/2 (11) [\overline{l}h\overline{k}]: −110/2 (12) [l\overline{h}\overline{k}]: −101/2

Point group: 432 Cubic Laue group: m[\overline{\bf{3}}]m
[P432] No. 207 (279)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
(5) [klh]: (6) [\overline{k}\overline{l}h]: (7) [\overline{k}l\overline{h}]: (8) [k\overline{l}\overline{h}]:
(9) [lhk]: (10) [\overline{l}\overline{h}k]: (11) [\overline{l}h\overline{k}]: (12) [l\overline{h}\overline{k}]:
(13) [kh\overline{l}]: (14) [\overline{k}\overline{h}\overline{l}]: (15) [\overline{k}hl]: (16) [k\overline{h}l]:
(17) [h\overline{l}k]: (18) [\overline{h}lk]: (19) [\overline{h}\overline{l}\overline{k}]: (20) [hl\overline{k}]:
(21) [\overline{l}kh]: (22) [l\overline{k}h]: (23) [lk\overline{h}]: (24) [\overline{l}\overline{k}\overline{h}]:
 
[P4_{2}32] No. 208 (280)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
(5) [klh]: (6) [\overline{k}\overline{l}h]: (7) [\overline{k}l\overline{h}]: (8) [k\overline{l}\overline{h}]:
(9) [lhk]: (10) [\overline{l}\overline{h}k]: (11) [\overline{l}h\overline{k}]: (12) [l\overline{h}\overline{k}]:
(13) [kh\overline{l}]: −111/2 (14) [\overline{k}\overline{h}\overline{l}]: −111/2 (15) [\overline{k}hl]: −111/2 (16) [k\overline{h}l]: −111/2
(17) [h\overline{l}k]: −111/2 (18) [\overline{h}lk]: −111/2 (19) [\overline{h}\overline{l}\overline{k}]: −111/2 (20) [hl\overline{k}]: −111/2
(21) [\overline{l}kh]: −111/2 (22) [l\overline{k}h]: −111/2 (23) [lk\overline{h}]: −111/2 (24) [\overline{l}\overline{k}\overline{h}]: −111/2
 
[F432] No. 209 (281)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
(5) [klh]: (6) [\overline{k}\overline{l}h]: (7) [\overline{k}l\overline{h}]: (8) [k\overline{l}\overline{h}]:
(9) [lhk]: (10) [\overline{l}\overline{h}k]: (11) [\overline{l}h\overline{k}]: (12) [l\overline{h}\overline{k}]:
(13) [kh\overline{l}]: (14) [\overline{k}\overline{h}\overline{l}]: (15) [\overline{k}hl]: (16) [k\overline{h}l]:
(17) [h\overline{l}k]: (18) [\overline{h}lk]: (19) [\overline{h}\overline{l}\overline{k}]: (20) [hl\overline{k}]:
(21) [\overline{l}kh]: (22) [l\overline{k}h]: (23) [lk\overline{h}]: (24) [\overline{l}\overline{k}\overline{h}]:
 
[F4_{1}32] No. 210 (282)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −011/2 (3) [\overline{h}k\overline{l}]: −110/2 (4) [h\overline{k}\overline{l}]: −101/2
(5) [klh]: (6) [\overline{k}\overline{l}h]: −101/2 (7) [\overline{k}l\overline{h}]: −011/2 (8) [k\overline{l}\overline{h}]: −110/2
(9) [lhk]: (10) [\overline{l}\overline{h}k]: −110/2 (11) [\overline{l}h\overline{k}]: −101/2 (12) [l\overline{h}\overline{k}]: −011/2
(13) [kh\overline{l}]: −313/4 (14) [\overline{k}\overline{h}\overline{l}]: −111/4 (15) [\overline{k}hl]: −133/4 (16) [k\overline{h}l]: −331/4
(17) [h\overline{l}k]: −313/4 (18) [\overline{h}lk]: −331/4 (19) [\overline{h}\overline{l}\overline{k}]: −111/4 (20) [hl\overline{k}]: −133/4
(21) [\overline{l}kh]: −313/4 (22) [l\overline{k}h]: −133/4 (23) [lk\overline{h}]: −331/4 (24) [\overline{l}\overline{k}\overline{h}]: −111/4
 
[I432] No. 211 (283)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
(5) [klh]: (6) [\overline{k}\overline{l}h]: (7) [\overline{k}l\overline{h}]: (8) [k\overline{l}\overline{h}]:
(9) [lhk]: (10) [\overline{l}\overline{h}k]: (11) [\overline{l}h\overline{k}]: (12) [l\overline{h}\overline{k}]:
(13) [kh\overline{l}]: (14) [\overline{k}\overline{h}\overline{l}]: (15) [\overline{k}hl]: (16) [k\overline{h}l]:
(17) [h\overline{l}k]: (18) [\overline{h}lk]: (19) [\overline{h}\overline{l}\overline{k}]: (20) [hl\overline{k}]:
(21) [\overline{l}kh]: (22) [l\overline{k}h]: (23) [lk\overline{h}]: (24) [\overline{l}\overline{k}\overline{h}]:
 
[P4_{3}32] No. 212 (284)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −101/2 (3) [\overline{h}k\overline{l}]: −011/2 (4) [h\overline{k}\overline{l}]: −110/2
(5) [klh]: (6) [\overline{k}\overline{l}h]: −110/2 (7) [\overline{k}l\overline{h}]: −101/2 (8) [k\overline{l}\overline{h}]: −011/2
(9) [lhk]: (10) [\overline{l}\overline{h}k]: −011/2 (11) [\overline{l}h\overline{k}]: −110/2 (12) [l\overline{h}\overline{k}]: −101/2
(13) [kh\overline{l}]: −133/4 (14) [\overline{k}\overline{h}\overline{l}]: −111/4 (15) [\overline{k}hl]: −331/4 (16) [k\overline{h}l]: −313/4
(17) [h\overline{l}k]: −133/4 (18) [\overline{h}lk]: −313/4 (19) [\overline{h}\overline{l}\overline{k}]: −111/4 (20) [hl\overline{k}]: −331/4
(21) [\overline{l}kh]: −133/4 (22) [l\overline{k}h]: −331/4 (23) [lk\overline{h}]: −313/4 (24) [\overline{l}\overline{k}\overline{h}]: −111/4
 
[P4_{1}32] No. 213 (285)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −101/2 (3) [\overline{h}k\overline{l}]: −011/2 (4) [h\overline{k}\overline{l}]: −110/2
(5) [klh]: (6) [\overline{k}\overline{l}h]: −110/2 (7) [\overline{k}l\overline{h}]: −101/2 (8) [k\overline{l}\overline{h}]: −011/2
(9) [lhk]: (10) [\overline{l}\overline{h}k]: −011/2 (11) [\overline{l}h\overline{k}]: −110/2 (12) [l\overline{h}\overline{k}]: −101/2
(13) [kh\overline{l}]: −311/4 (14) [\overline{k}\overline{h}\overline{l}]: −333/4 (15) [\overline{k}hl]: −113/4 (16) [k\overline{h}l]: −131/4
(17) [h\overline{l}k]: −311/4 (18) [\overline{h}lk]: −131/4 (19) [\overline{h}\overline{l}\overline{k}]: −333/4 (20) [hl\overline{k}]: −113/4
(21) [\overline{l}kh]: −311/4 (22) [l\overline{k}h]: −113/4 (23) [lk\overline{h}]: −131/4 (24) [\overline{l}\overline{k}\overline{h}]: −333/4
 
[I4_{1}32] No. 214 (286)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −101/2 (3) [\overline{h}k\overline{l}]: −011/2 (4) [h\overline{k}\overline{l}]: −110/2
(5) [klh]: (6) [\overline{k}\overline{l}h]: −110/2 (7) [\overline{k}l\overline{h}]: −101/2 (8) [k\overline{l}\overline{h}]: −011/2
(9) [lhk]: (10) [\overline{l}\overline{h}k]: −011/2 (11) [\overline{l}h\overline{k}]: −110/2 (12) [l\overline{h}\overline{k}]: −101/2
(13) [kh\overline{l}]: −311/4 (14) [\overline{k}\overline{h}\overline{l}]: −333/4 (15) [\overline{k}hl]: −113/4 (16) [k\overline{h}l]: −131/4
(17) [h\overline{l}k]: −311/4 (18) [\overline{h}lk]: −131/4 (19) [\overline{h}\overline{l}\overline{k}]: −333/4 (20) [hl\overline{k}]: −113/4
(21) [\overline{l}kh]: −311/4 (22) [l\overline{k}h]: −113/4 (23) [lk\overline{h}]: −131/4 (24) [\overline{l}\overline{k}\overline{h}]: −333/4

Point group: [\bf{{\overline{4}}}]3m Cubic Laue group: m[\overline{\bf{3}}]m
[P\overline{4}3m] No. 215 (287)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
(5) [klh]: (6) [\overline{k}\overline{l}h]: (7) [\overline{k}l\overline{h}]: (8) [k\overline{l}\overline{h}]:
(9) [lhk]: (10) [\overline{l}\overline{h}k]: (11) [\overline{l}h\overline{k}]: (12) [l\overline{h}\overline{k}]:
(13) [khl]: (14) [\overline{k}\overline{h}l]: (15) [\overline{k}h\overline{l}]: (16) [k\overline{h}\overline{l}]:
(17) [hlk]: (18) [\overline{h}\overline{l}k]: (19) [\overline{h}l\overline{k}]: (20) [h\overline{l}\overline{k}]:
(21) [lkh]: (22) [\overline{l}\overline{k}h]: (23) [\overline{l}k\overline{h}]: (24) [l\overline{k}\overline{h}]:
 
[F\overline{4}3m] No. 216 (288)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
(5) [klh]: (6) [\overline{k}\overline{l}h]: (7) [\overline{k}l\overline{h}]: (8) [k\overline{l}\overline{h}]:
(9) [lhk]: (10) [\overline{l}\overline{h}k]: (11) [\overline{l}h\overline{k}]: (12) [l\overline{h}\overline{k}]:
(13) [khl]: (14) [\overline{k}\overline{h}l]: (15) [\overline{k}h\overline{l}]: (16) [k\overline{h}\overline{l}]:
(17) [hlk]: (18) [\overline{h}\overline{l}k]: (19) [\overline{h}l\overline{k}]: (20) [h\overline{l}\overline{k}]:
(21) [lkh]: (22) [\overline{l}\overline{k}h]: (23) [\overline{l}k\overline{h}]: (24) [l\overline{k}\overline{h}]:
 
[I\overline{4}3m] No. 217 (289)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
(5) [klh]: (6) [\overline{k}\overline{l}h]: (7) [\overline{k}l\overline{h}]: (8) [k\overline{l}\overline{h}]:
(9) [lhk]: (10) [\overline{l}\overline{h}k]: (11) [\overline{l}h\overline{k}]: (12) [l\overline{h}\overline{k}]:
(13) [khl]: (14) [\overline{k}\overline{h}l]: (15) [\overline{k}h\overline{l}]: (16) [k\overline{h}\overline{l}]:
(17) [hlk]: (18) [\overline{h}\overline{l}k]: (19) [\overline{h}l\overline{k}]: (20) [h\overline{l}\overline{k}]:
(21) [lkh]: (22) [\overline{l}\overline{k}h]: (23) [\overline{l}k\overline{h}]: (24) [l\overline{k}\overline{h}]:
 
[P\overline{4}3n] No. 218 (290)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
(5) [klh]: (6) [\overline{k}\overline{l}h]: (7) [\overline{k}l\overline{h}]: (8) [k\overline{l}\overline{h}]:
(9) [lhk]: (10) [\overline{l}\overline{h}k]: (11) [\overline{l}h\overline{k}]: (12) [l\overline{h}\overline{k}]:
(13) [khl]: −111/2 (14) [\overline{k}\overline{h}l]: −111/2 (15) [\overline{k}h\overline{l}]: −111/2 (16) [k\overline{h}\overline{l}]: −111/2
(17) [hlk]: −111/2 (18) [\overline{h}\overline{l}k]: −111/2 (19) [\overline{h}l\overline{k}]: −111/2 (20) [h\overline{l}\overline{k}]: −111/2
(21) [lkh]: −111/2 (22) [\overline{l}\overline{k}h]: −111/2 (23) [\overline{l}k\overline{h}]: −111/2 (24) [l\overline{k}\overline{h}]: −111/2
 
[F\overline{4}3c] No. 219 (291)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
(5) [klh]: (6) [\overline{k}\overline{l}h]: (7) [\overline{k}l\overline{h}]: (8) [k\overline{l}\overline{h}]:
(9) [lhk]: (10) [\overline{l}\overline{h}k]: (11) [\overline{l}h\overline{k}]: (12) [l\overline{h}\overline{k}]:
(13) [khl]: −111/2 (14) [\overline{k}\overline{h}l]: −111/2 (15) [\overline{k}h\overline{l}]: −111/2 (16) [k\overline{h}\overline{l}]: −111/2
(17) [hlk]: −111/2 (18) [\overline{h}\overline{l}k]: −111/2 (19) [\overline{h}l\overline{k}]: −111/2 (20) [h\overline{l}\overline{k}]: −111/2
(21) [lkh]: −111/2 (22) [\overline{l}\overline{k}h]: −111/2 (23) [\overline{l}k\overline{h}]: −111/2 (24) [l\overline{k}\overline{h}]: −111/2
 
[I\overline{4}3d] No. 220 (292)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −010/2 (3) [\overline{h}k\overline{l}]: −011/2 (4) [h\overline{k}\overline{l}]: −001/2
(5) [klh]: (6) [\overline{k}\overline{l}h]: −001/2 (7) [\overline{k}l\overline{h}]: −101/2 (8) [k\overline{l}\overline{h}]: −100/2
(9) [lhk]: (10) [\overline{l}\overline{h}k]: −100/2 (11) [\overline{l}h\overline{k}]: −110/2 (12) [l\overline{h}\overline{k}]: −010/2
(13) [khl]: −111/4 (14) [\overline{k}\overline{h}l]: −311/4 (15) [\overline{k}h\overline{l}]: −313/4 (16) [k\overline{h}\overline{l}]: −113/4
(17) [hlk]: −111/4 (18) [\overline{h}\overline{l}k]: −113/4 (19) [\overline{h}l\overline{k}]: −133/4 (20) [h\overline{l}\overline{k}]: −131/4
(21) [lkh]: −111/4 (22) [\overline{l}\overline{k}h]: −131/4 (23) [\overline{l}k\overline{h}]: −331/4 (24) [l\overline{k}\overline{h}]: −311/4

Point group: m[\overline{\bf{3}}]m Cubic Laue group: m[\overline{\bf{3}}]m
[Pm\overline{3}m] No. 221 (293)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
(5) [klh]: (6) [\overline{k}\overline{l}h]: (7) [\overline{k}l\overline{h}]: (8) [k\overline{l}\overline{h}]:
(9) [lhk]: (10) [\overline{l}\overline{h}k]: (11) [\overline{l}h\overline{k}]: (12) [l\overline{h}\overline{k}]:
(13) [kh\overline{l}]: (14) [\overline{k}\overline{h}\overline{l}]: (15) [\overline{k}hl]: (16) [k\overline{h}l]:
(17) [h\overline{l}k]: (18) [\overline{h}lk]: (19) [\overline{h}\overline{l}\overline{k}]: (20) [hl\overline{k}]:
(21) [\overline{l}kh]: (22) [l\overline{k}h]: (23) [lk\overline{h}]: (24) [\overline{l}\overline{k}\overline{h}]:
 
[Pn\overline{3}n] Origin 1 No. 222 (294)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
(5) [klh]: (6) [\overline{k}\overline{l}h]: (7) [\overline{k}l\overline{h}]: (8) [k\overline{l}\overline{h}]:
(9) [lhk]: (10) [\overline{l}\overline{h}k]: (11) [\overline{l}h\overline{k}]: (12) [l\overline{h}\overline{k}]:
(13) [kh\overline{l}]: (14) [\overline{k}\overline{h}\overline{l}]: (15) [\overline{k}hl]: (16) [k\overline{h}l]:
(17) [h\overline{l}k]: (18) [\overline{h}lk]: (19) [\overline{h}\overline{l}\overline{k}]: (20) [hl\overline{k}]:
(21) [\overline{l}kh]: (22) [l\overline{k}h]: (23) [lk\overline{h}]: (24) [\overline{l}\overline{k}\overline{h}]:
(25) [\overline{h}\overline{k}\overline{l}]: −111/2 (26) [hk\overline{l}]: −111/2 (27) [h\overline{k}l]: −111/2 (28) [\overline{h}kl]: −111/2
(29) [\overline{k}\overline{l}\overline{h}]: −111/2 (30) [kl\overline{h}]: −111/2 (31) [k\overline{l}h]: −111/2 (32) [\overline{k}lh]: −111/2
(33) [\overline{l}\overline{h}\overline{k}]: −111/2 (34) [lh\overline{k}]: −111/2 (35) [l\overline{h}k]: −111/2 (36) [\overline{l}hk]: −111/2
(37) [\overline{k}\overline{h}l]: −111/2 (38) [khl]: −111/2 (39) [k\overline{h}\overline{l}]: −111/2 (40) [\overline{k}h\overline{l}]: −111/2
(41) [\overline{h}l\overline{k}]: −111/2 (42) [h\overline{l}\overline{k}]: −111/2 (43) [hlk]: −111/2 (44) [\overline{h}\overline{l}k]: −111/2
(45) [l\overline{k}\overline{h}]: −111/2 (46) [\overline{l}k\overline{h}]: −111/2 (47) [\overline{l}\overline{k}h]: −111/2 (48) [lkh]: −111/2
 
[Pn\overline{3}n] Origin 2 No. 222 (295)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −110/2 (3) [\overline{h}k\overline{l}]: −101/2 (4) [h\overline{k}\overline{l}]: −011/2
(5) [klh]: (6) [\overline{k}\overline{l}h]: −011/2 (7) [\overline{k}l\overline{h}]: −110/2 (8) [k\overline{l}\overline{h}]: −101/2
(9) [lhk]: (10) [\overline{l}\overline{h}k]: −101/2 (11) [\overline{l}h\overline{k}]: −011/2 (12) [l\overline{h}\overline{k}]: −110/2
(13) [kh\overline{l}]: −001/2 (14) [\overline{k}\overline{h}\overline{l}]: −111/2 (15) [\overline{k}hl]: −010/2 (16) [k\overline{h}l]: −100/2
(17) [h\overline{l}k]: −001/2 (18) [\overline{h}lk]: −100/2 (19) [\overline{h}\overline{l}\overline{k}]: −111/2 (20) [hl\overline{k}]: −010/2
(21) [\overline{l}kh]: −001/2 (22) [l\overline{k}h]: −010/2 (23) [lk\overline{h}]: −100/2 (24) [\overline{l}\overline{k}\overline{h}]: −111/2
 
[Pm\overline{3}n] No. 223 (296)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
(5) [klh]: (6) [\overline{k}\overline{l}h]: (7) [\overline{k}l\overline{h}]: (8) [k\overline{l}\overline{h}]:
(9) [lhk]: (10) [\overline{l}\overline{h}k]: (11) [\overline{l}h\overline{k}]: (12) [l\overline{h}\overline{k}]:
(13) [kh\overline{l}]: −111/2 (14) [\overline{k}\overline{h}\overline{l}]: −111/2 (15) [\overline{k}hl]: −111/2 (16) [k\overline{h}l]: −111/2
(17) [h\overline{l}k]: −111/2 (18) [\overline{h}lk]: −111/2 (19) [\overline{h}\overline{l}\overline{k}]: −111/2 (20) [hl\overline{k}]: −111/2
(21) [\overline{l}kh]: −111/2 (22) [l\overline{k}h]: −111/2 (23) [lk\overline{h}]: −111/2 (24) [\overline{l}\overline{k}\overline{h}]: −111/2
 
[Pn\overline{3}m] Origin 1 No. 224 (297)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
(5) [klh]: (6) [\overline{k}\overline{l}h]: (7) [\overline{k}l\overline{h}]: (8) [k\overline{l}\overline{h}]:
(9) [lhk]: (10) [\overline{l}\overline{h}k]: (11) [\overline{l}h\overline{k}]: (12) [l\overline{h}\overline{k}]:
(13) [kh\overline{l}]: −111/2 (14) [\overline{k}\overline{h}\overline{l}]: −111/2 (15) [\overline{k}hl]: −111/2 (16) [k\overline{h}l]: −111/2
(17) [h\overline{l}k]: −111/2 (18) [\overline{h}lk]: −111/2 (19) [\overline{h}\overline{l}\overline{k}]: −111/2 (20) [hl\overline{k}]: −111/2
(21) [\overline{l}kh]: −111/2 (22) [l\overline{k}h]: −111/2 (23) [lk\overline{h}]: −111/2 (24) [\overline{l}\overline{k}\overline{h}]: −111/2
(25) [\overline{h}\overline{k}\overline{l}]: −111/2 (26) [hk\overline{l}]: −111/2 (27) [h\overline{k}l]: −111/2 (28) [\overline{h}kl]: −111/2
(29) [\overline{k}\overline{l}\overline{h}]: −111/2 (30) [kl\overline{h}]: −111/2 (31) [k\overline{l}h]: −111/2 (32) [\overline{k}lh]: −111/2
(33) [\overline{l}\overline{h}\overline{k}]: −111/2 (34) [lh\overline{k}]: −111/2 (35) [l\overline{h}k]: −111/2 (36) [\overline{l}hk]: −111/2
(37) [\overline{k}\overline{h}l]: (38) [khl]: (39) [k\overline{h}\overline{l}]: (40) [\overline{k}h\overline{l}]:
(41) [\overline{h}l\overline{k}]: (42) [h\overline{l}\overline{k}]: (43) [hlk]: (44) [\overline{h}\overline{l}k]:
(45) [l\overline{k}\overline{h}]: (46) [\overline{l}k\overline{h}]: (47) [\overline{l}\overline{k}h]: (48) [lkh]:
 
[Pn\overline{3}m] Origin 2 No. 224 (298)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −110/2 (3) [\overline{h}k\overline{l}]: −101/2 (4) [h\overline{k}\overline{l}]: −011/2
(5) [klh]: (6) [\overline{k}\overline{l}h]: −011/2 (7) [\overline{k}l\overline{h}]: −110/2 (8) [k\overline{l}\overline{h}]: −101/2
(9) [lhk]: (10) [\overline{l}\overline{h}k]: −101/2 (11) [\overline{l}h\overline{k}]: −011/2 (12) [l\overline{h}\overline{k}]: −110/2
(13) [kh\overline{l}]: −110/2 (14) [\overline{k}\overline{h}\overline{l}]: (15) [\overline{k}hl]: −101/2 (16) [k\overline{h}l]: −011/2
(17) [h\overline{l}k]: −110/2 (18) [\overline{h}lk]: −011/2 (19) [\overline{h}\overline{l}\overline{k}]: (20) [hl\overline{k}]: −101/2
(21) [\overline{l}kh]: −110/2 (22) [l\overline{k}h]: −101/2 (23) [lk\overline{h}]: −011/2 (24) [\overline{l}\overline{k}\overline{h}]:
 
[Fm\overline{3}m] No. 225 (299)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
(5) [klh]: (6) [\overline{k}\overline{l}h]: (7) [\overline{k}l\overline{h}]: (8) [k\overline{l}\overline{h}]:
(9) [lhk]: (10) [\overline{l}\overline{h}k]: (11) [\overline{l}h\overline{k}]: (12) [l\overline{h}\overline{k}]:
(13) [kh\overline{l}]: (14) [\overline{k}\overline{h}\overline{l}]: (15) [\overline{k}hl]: (16) [k\overline{h}l]:
(17) [h\overline{l}k]: (18) [\overline{h}lk]: (19) [\overline{h}\overline{l}\overline{k}]: (20) [hl\overline{k}]:
(21) [\overline{l}kh]: (22) [l\overline{k}h]: (23) [lk\overline{h}]: (24) [\overline{l}\overline{k}\overline{h}]:
 
[Fm\overline{3}c] No. 226 (300)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
(5) [klh]: (6) [\overline{k}\overline{l}h]: (7) [\overline{k}l\overline{h}]: (8) [k\overline{l}\overline{h}]:
(9) [lhk]: (10) [\overline{l}\overline{h}k]: (11) [\overline{l}h\overline{k}]: (12) [l\overline{h}\overline{k}]:
(13) [kh\overline{l}]: −111/2 (14) [\overline{k}\overline{h}\overline{l}]: −111/2 (15) [\overline{k}hl]: −111/2 (16) [k\overline{h}l]: −111/2
(17) [h\overline{l}k]: −111/2 (18) [\overline{h}lk]: −111/2 (19) [\overline{h}\overline{l}\overline{k}]: −111/2 (20) [hl\overline{k}]: −111/2
(21) [\overline{l}kh]: −111/2 (22) [l\overline{k}h]: −111/2 (23) [lk\overline{h}]: −111/2 (24) [\overline{l}\overline{k}\overline{h}]: −111/2
 
[Fd\overline{3}m] Origin 1 No. 227 (301)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −011/2 (3) [\overline{h}k\overline{l}]: −110/2 (4) [h\overline{k}\overline{l}]: −101/2
(5) [klh]: (6) [\overline{k}\overline{l}h]: −101/2 (7) [\overline{k}l\overline{h}]: −011/2 (8) [k\overline{l}\overline{h}]: −110/2
(9) [lhk]: (10) [\overline{l}\overline{h}k]: −110/2 (11) [\overline{l}h\overline{k}]: −101/2 (12) [l\overline{h}\overline{k}]: −011/2
(13) [kh\overline{l}]: −313/4 (14) [\overline{k}\overline{h}\overline{l}]: −111/4 (15) [\overline{k}hl]: −133/4 (16) [k\overline{h}l]: −331/4
(17) [h\overline{l}k]: −313/4 (18) [\overline{h}lk]: −331/4 (19) [\overline{h}\overline{l}\overline{k}]: −111/4 (20) [hl\overline{k}]: −133/4
(21) [\overline{l}kh]: −313/4 (22) [l\overline{k}h]: −133/4 (23) [lk\overline{h}]: −331/4 (24) [\overline{l}\overline{k}\overline{h}]: −111/4
(25) [\overline{h}\overline{k}\overline{l}]: −111/4 (26) [hk\overline{l}]: −133/4 (27) [h\overline{k}l]: −331/4 (28) [\overline{h}kl]: −313/4
(29) [\overline{k}\overline{l}\overline{h}]: −111/4 (30) [kl\overline{h}]: −313/4 (31) [k\overline{l}h]: −133/4 (32) [\overline{k}lh]: −331/4
(33) [\overline{l}\overline{h}\overline{k}]: −111/4 (34) [lh\overline{k}]: −331/4 (35) [l\overline{h}k]: −313/4 (36) [\overline{l}hk]: −133/4
(37) [\overline{k}\overline{h}l]: −101/2 (38) [khl]: (39) [k\overline{h}\overline{l}]: −011/2 (40) [\overline{k}h\overline{l}]: −110/2
(41) [\overline{h}l\overline{k}]: −101/2 (42) [h\overline{l}\overline{k}]: −110/2 (43) [hlk]: (44) [\overline{h}\overline{l}k]: −011/2
(45) [l\overline{k}\overline{h}]: −101/2 (46) [\overline{l}k\overline{h}]: −011/2 (47) [\overline{l}\overline{k}h]: −110/2 (48) [lkh]:
 
[Fd\overline{3}m] Origin 2 No. 227 (302)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −312/4 (3) [\overline{h}k\overline{l}]: −123/4 (4) [h\overline{k}\overline{l}]: −231/4
(5) [klh]: (6) [\overline{k}\overline{l}h]: −231/4 (7) [\overline{k}l\overline{h}]: −312/4 (8) [k\overline{l}\overline{h}]: −123/4
(9) [lhk]: (10) [\overline{l}\overline{h}k]: −123/4 (11) [\overline{l}h\overline{k}]: −231/4 (12) [l\overline{h}\overline{k}]: −312/4
(13) [kh\overline{l}]: −312/4 (14) [\overline{k}\overline{h}\overline{l}]: (15) [\overline{k}hl]: −123/4 (16) [k\overline{h}l]: −231/4
(17) [h\overline{l}k]: −312/4 (18) [\overline{h}lk]: −231/4 (19) [\overline{h}\overline{l}\overline{k}]: (20) [hl\overline{k}]: −123/4
(21) [\overline{l}kh]: −312/4 (22) [l\overline{k}h]: −123/4 (23) [lk\overline{h}]: −231/4 (24) [\overline{l}\overline{k}\overline{h}]:
 
[Fd\overline{3}c] Origin 1 No. 228 (303)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −011/2 (3) [\overline{h}k\overline{l}]: −110/2 (4) [h\overline{k}\overline{l}]: −101/2
(5) [klh]: (6) [\overline{k}\overline{l}h]: −101/2 (7) [\overline{k}l\overline{h}]: −011/2 (8) [k\overline{l}\overline{h}]: −110/2
(9) [lhk]: (10) [\overline{l}\overline{h}k]: −110/2 (11) [\overline{l}h\overline{k}]: −101/2 (12) [l\overline{h}\overline{k}]: −011/2
(13) [kh\overline{l}]: −313/4 (14) [\overline{k}\overline{h}\overline{l}]: −111/4 (15) [\overline{k}hl]: −133/4 (16) [k\overline{h}l]: −331/4
(17) [h\overline{l}k]: −313/4 (18) [\overline{h}lk]: −331/4 (19) [\overline{h}\overline{l}\overline{k}]: −111/4 (20) [hl\overline{k}]: −133/4
(21) [\overline{l}kh]: −313/4 (22) [l\overline{k}h]: −133/4 (23) [lk\overline{h}]: −331/4 (24) [\overline{l}\overline{k}\overline{h}]: −111/4
(25) [\overline{h}\overline{k}\overline{l}]: −333/4 (26) [hk\overline{l}]: −311/4 (27) [h\overline{k}l]: −113/4 (28) [\overline{h}kl]: −131/4
(29) [\overline{k}\overline{l}\overline{h}]: −333/4 (30) [kl\overline{h}]: −131/4 (31) [k\overline{l}h]: −311/4 (32) [\overline{k}lh]: −113/4
(33) [\overline{l}\overline{h}\overline{k}]: −333/4 (34) [lh\overline{k}]: −113/4 (35) [l\overline{h}k]: −131/4 (36) [\overline{l}hk]: −311/4
(37) [\overline{k}\overline{h}l]: −010/2 (38) [khl]: −111/2 (39) [k\overline{h}\overline{l}]: −100/2 (40) [\overline{k}h\overline{l}]: −001/2
(41) [\overline{h}l\overline{k}]: −010/2 (42) [h\overline{l}\overline{k}]: −001/2 (43) [hlk]: −111/2 (44) [\overline{h}\overline{l}k]: −100/2
(45) [l\overline{k}\overline{h}]: −010/2 (46) [\overline{l}k\overline{h}]: −100/2 (47) [\overline{l}\overline{k}h]: −001/2 (48) [lkh]: −111/2
 
[Fd\overline{3}c] Origin 2 No. 228 (304)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −132/4 (3) [\overline{h}k\overline{l}]: −321/4 (4) [h\overline{k}\overline{l}]: −213/4
(5) [klh]: (6) [\overline{k}\overline{l}h]: −213/4 (7) [\overline{k}l\overline{h}]: −132/4 (8) [k\overline{l}\overline{h}]: −321/4
(9) [lhk]: (10) [\overline{l}\overline{h}k]: −321/4 (11) [\overline{l}h\overline{k}]: −213/4 (12) [l\overline{h}\overline{k}]: −132/4
(13) [kh\overline{l}]: −310/4 (14) [\overline{k}\overline{h}\overline{l}]: −111/2 (15) [\overline{k}hl]: −103/4 (16) [k\overline{h}l]: −031/4
(17) [h\overline{l}k]: −310/4 (18) [\overline{h}lk]: −031/4 (19) [\overline{h}\overline{l}\overline{k}]: −111/2 (20) [hl\overline{k}]: −103/4
(21) [\overline{l}kh]: −310/4 (22) [l\overline{k}h]: −103/4 (23) [lk\overline{h}]: −031/4 (24) [\overline{l}\overline{k}\overline{h}]: −111/2
 
[Im\overline{3}m] No. 229 (305)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: (3) [\overline{h}k\overline{l}]: (4) [h\overline{k}\overline{l}]:
(5) [klh]: (6) [\overline{k}\overline{l}h]: (7) [\overline{k}l\overline{h}]: (8) [k\overline{l}\overline{h}]:
(9) [lhk]: (10) [\overline{l}\overline{h}k]: (11) [\overline{l}h\overline{k}]: (12) [l\overline{h}\overline{k}]:
(13) [kh\overline{l}]: (14) [\overline{k}\overline{h}\overline{l}]: (15) [\overline{k}hl]: (16) [k\overline{h}l]:
(17) [h\overline{l}k]: (18) [\overline{h}lk]: (19) [\overline{h}\overline{l}\overline{k}]: (20) [hl\overline{k}]:
(21) [\overline{l}kh]: (22) [l\overline{k}h]: (23) [lk\overline{h}]: (24) [\overline{l}\overline{k}\overline{h}]:
 
[Ia\overline{3}d] No. 230 (306)
(1) [hkl]: (2) [\overline{h}\overline{k}l]: −101/2 (3) [\overline{h}k\overline{l}]: −011/2 (4) [h\overline{k}\overline{l}]: −110/2
(5) [klh]: (6) [\overline{k}\overline{l}h]: −110/2 (7) [\overline{k}l\overline{h}]: −101/2 (8) [k\overline{l}\overline{h}]: −011/2
(9) [lhk]: (10) [\overline{l}\overline{h}k]: −011/2 (11) [\overline{l}h\overline{k}]: −110/2 (12) [l\overline{h}\overline{k}]: −101/2
(13) [kh\overline{l}]: −311/4 (14) [\overline{k}\overline{h}\overline{l}]: −333/4 (15) [\overline{k}hl]: −113/4 (16) [k\overline{h}l]: −131/4
(17) [h\overline{l}k]: −311/4 (18) [\overline{h}lk]: −131/4 (19) [\overline{h}\overline{l}\overline{k}]: −333/4 (20) [hl\overline{k}]: −113/4
(21) [\overline{l}kh]: −311/4 (22) [l\overline{k}h]: −113/4 (23) [lk\overline{h}]: −131/4 (24) [\overline{l}\overline{k}\overline{h}]: −333/4

References

International Tables for X-ray Crystallography (1952). Vol. I. Symmetry groups, edited by N. F. M. Henry & K. Lonsdale. Birmingham: Kynoch Press.








































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