| C2 | C23 | 2 | Monoclinic  |
| No. 5 | C121 | Patterson symmetry C12/m1 | |
| UNIQUE AXIS b, CELL CHOICE 1 | |||
Origin on 2
| Asymmetric unit | 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1 |
Symmetry operations
For (0, 0, 0)+ set
| (1) 1 | (2) 2 0, y, 0 |
For (1/2, 1/2, 0)+ set
| (1) t(1/2, 1/2, 0) | (2) 2(0, 1/2, 0) 1/4, y, 0 |
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/2, 1/2, 0); (2)
Positions
| Multiplicity, Wyckoff letter, Site symmetry | Coordinates | Reflection conditions | |||||
| (0, 0, 0)+ (1/2, 1/2, 0)+ | General: | ||||||
|
| hkl : h + k = 2n h0l : h = 2n 0kl : k = 2n hk0 : h + k = 2n 0k0 : k = 2n h00 : h = 2n |
| Special: as above, plus | ||||||
|
| no extra conditions | ||||
|
| no extra conditions |
Symmetry of special projections
| Along [001] c1m1 a' = ap b' = b Origin at 0, 0, z | Along [100] p11m a' = 1/2b b' = cp Origin at x, 0, 0 | Along [010] p2 a' = c b' = 1/2a Origin at 0, y, 0 |
Maximal non-isomorphic subgroups
| I | [2] C1 (P1, 1) | 1+ |
| IIa | [2] P1211 (P21, 4) | 1; 2 + (1/2, 1/2, 0) | |
| [2] P121 (P2, 3) | 1; 2 |
| IIb | none |
Maximal isomorphic subgroups of lowest index
| IIc | [2] C121 (c' = 2c or a' = a + 2c, c' = 2c) (C2, 5); [3] C121 (b' = 3b) (C2, 5) |
Minimal non-isomorphic supergroups
| I | [2] C2/m (12); [2] C2/c (15); [2] C2221 (20); [2] C222 (21); [2] F222 (22); [2] I222 (23); [2] I212121 (24); [2] Amm2 (38); [2] Aem2 (39); [2] Ama2 (40); [2] Aea2 (41); [2] Fmm2 (42); [2] Fdd2 (43); [2] Imm2 (44); [2] Iba2 (45); [2] Ima2 (46); [2] I4 (79); [2] I41 (80); [2] I-4 (82); [3] P312 (149); [3] P321 (150); [3] P3112 (151); [3] P3121 (152); [3] P3212 (153); [3] P3221 (154); [3] R32 (155) |
| II | [2] P121 (a' = 1/2a, b' = 1/2b) (P2, 3) |
UNIQUE AXIS b, DIFFERENT CELL CHOICES
C121
UNIQUE AXIS b, CELL CHOICE 1
Origin on 2
| Asymmetric unit | 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1 |
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/2, 1/2, 0); (2)
Positions
| Multiplicity, Wyckoff letter, Site symmetry | Coordinates | Reflection conditions | ||||||
| (0, 0, 0)+ (1/2, 1/2, 0)+ | General: | |||||||
|
| hkl : h + k = 2n h0l : h = 2n 0kl : k = 2n hk0 : h + k = 2n 0k0 : k = 2n h00 : h = 2n |
| Special: as above, plus | ||||||
|
| no extra conditions | ||||
|
| no extra conditions |
A121
UNIQUE AXIS b, CELL CHOICE 2
Origin on 2
| Asymmetric unit | 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1 |
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(0, 1/2, 1/2); (2)
Positions
| Multiplicity, Wyckoff letter, Site symmetry | Coordinates | Reflection conditions | |||||
| (0, 0, 0)+ (0, 1/2, 1/2)+ | General: | ||||||
|
| hkl : k + l = 2n h0l : l = 2n 0kl : k + l = 2n hk0 : k = 2n 0k0 : k = 2n 00l : l = 2n |
| Special: as above, plus | ||||||
|
| no extra conditions | ||||
|
| no extra conditions |
I121
UNIQUE AXIS b, CELL CHOICE 3
Origin on 2
| Asymmetric unit | 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1 |
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/2, 1/2, 1/2); (2)
Positions
| Multiplicity, Wyckoff letter, Site symmetry | Coordinates | Reflection conditions | ||||||
| (0, 0, 0)+ (1/2, 1/2, 1/2)+ | General: | |||||||
|
| hkl : h + k + l = 2n h0l : h + l = 2n 0kl : k + l = 2n hk0 : h + k = 2n 0k0 : k = 2n h00 : h = 2n 00l : l = 2n |
| Special: as above, plus | ||||||
|
| no extra conditions | ||||
|
| no extra conditions |
| C2 | C23 | 2 | Monoclinic |
| No. 5 | A112 | Patterson symmetry A112/m | |
| UNIQUE AXIS c, CELL CHOICE 1 | |||
Origin on 2
| Asymmetric unit | 0 ≤ x ≤ 1; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1/2 |
Symmetry operations
For (0, 0, 0)+ set
| (1) 1 | (2) 2 0, 0, z |
For (0, 1/2, 1/2)+ set
| (1) t(0, 1/2, 1/2) | (2) 2(0, 0, 1/2) 0, 1/4, z |
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(0, 1/2, 1/2); (2)
Positions
| Multiplicity, Wyckoff letter, Site symmetry | Coordinates | Reflection conditions | |||||
| (0, 0, 0)+ (0, 1/2, 1/2)+ | General: | ||||||
|
| hkl : k + l = 2n hk0 : k = 2n 0kl : k + l = 2n h0l : l = 2n 00l : l = 2n 0k0 : k = 2n |
| Special: as above, plus | ||||||
|
| no extra conditions | ||||
|
| no extra conditions |
Symmetry of special projections
| Along [001] p2 a' = a b' = 1/2b Origin at 0, 0, z | Along [100] c1m1 a' = bp b' = c Origin at x, 0, 0 | Along [010] p11m a' = 1/2c b' = ap Origin at 0, y, 0 |
Maximal non-isomorphic subgroups
| I | [2] A1 (P1, 1) | 1+ |
| IIa | [2] P1121 (P21, 4) | 1; 2 + (0, 1/2, 1/2) | |
| [2] P112 (P2, 3) | 1; 2 |
| IIb | none |
Maximal isomorphic subgroups of lowest index
| IIc | [2] A112 (a' = 2a or a' = 2a, b' = 2a + b) (C2, 5); [3] A112 (c' = 3c) (C2, 5) |
Minimal non-isomorphic supergroups
| I | [2] C2/m (12); [2] C2/c (15); [2] C2221 (20); [2] C222 (21); [2] F222 (22); [2] I222 (23); [2] I212121 (24); [2] Amm2 (38); [2] Aem2 (39); [2] Ama2 (40); [2] Aea2 (41); [2] Fmm2 (42); [2] Fdd2 (43); [2] Imm2 (44); [2] Iba2 (45); [2] Ima2 (46); [2] I4 (79); [2] I41 (80); [2] I-4 (82); [3] P312 (149); [3] P321 (150); [3] P3112 (151); [3] P3121 (152); [3] P3212 (153); [3] P3221 (154); [3] R32 (155) |
| II | [2] P112 (b' = 1/2b, c' = 1/2c) (P2, 3) |
UNIQUE AXIS c, DIFFERENT CELL CHOICES
A112
UNIQUE AXIS c, CELL CHOICE 1
Origin on 2
| Asymmetric unit | 0 ≤ x ≤ 1; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1/2 |
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(0, 1/2, 1/2); (2)
Positions
| Multiplicity, Wyckoff letter, Site symmetry | Coordinates | Reflection conditions | |||||
| (0, 0, 0)+ (0, 1/2, 1/2)+ | General: | ||||||
|
| hkl : k + l = 2n hk0 : k = 2n 0kl : k + l = 2n h0l : l = 2n 00l : l = 2n 0k0 : k = 2n |
| Special: as above, plus | ||||||
|
| no extra conditions | ||||
|
| no extra conditions |
B112
UNIQUE AXIS c, CELL CHOICE 2
Origin on 2
| Asymmetric unit | 0 ≤ x ≤ 1; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1/2 |
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/2, 0, 1/2); (2)
Positions
| Multiplicity, Wyckoff letter, Site symmetry | Coordinates | Reflection conditions | |||||
| (0, 0, 0)+ (1/2, 0, 1/2)+ | General: | ||||||
|
| hkl : h + l = 2n hk0 : h = 2n 0kl : l = 2n h0l : h + l = 2n 00l : l = 2n h00 : h = 2n |
| Special: as above, plus | ||||||
|
| no extra conditions | ||||
|
| no extra conditions |
I112
UNIQUE AXIS c, CELL CHOICE 3
Origin on 2
| Asymmetric unit | 0 ≤ x ≤ 1; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1/2 |
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/2, 1/2, 1/2); (2)
Positions
| Multiplicity, Wyckoff letter, Site symmetry | Coordinates | Reflection conditions | |||||
| (0, 0, 0)+ (1/2, 1/2, 1/2)+ | General: | ||||||
|
| hkl : h + k + l = 2n hk0 : h + k = 2n 0kl : k + l = 2n h0l : h + l = 2n 00l : l = 2n h00 : h = 2n 0k0 : k = 2n |
| Special: as above, plus | ||||||
|
| no extra conditions | ||||
|
| no extra conditions |
