| P21/m | No. 11 | C2h2 |
| P 1 21/m 1 | ||||||||
|
UNIQUE AXIS b |
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| Axes | Coordinates | Wyckoff positions | ||||||
| 2a | 2b | 2c | 2d | 2e | 4f | |||
| I Maximal translationengleiche subgroups | ||||||||
| [2] P1m1 (6) | x, y + (1/4), z | 2c | 2c | 2c | 2c | 1a; 1b | 2 × 2c | |
| [2] P1211 (4) | 2a | 2a | 2a | 2a | 2a | 2 × 2a | ||
| [2] P-1 (2) | 1a; 1c | 1d; 1e | 1b; 1g | 1f; 1h | 2i | 2 × 2i | ||
| II Maximal klassengleiche subgroups | ||||||||
| Enlarged unit cell, non-isomorphic | ||||||||
| [2] P121/a1 (14) | 2a, b, c | (1/2)x, y, z; +((1/2), 0, 0) | 2a; 2c | 4e | 2b; 2d | 4e | 4e | 2 × 4e |
| [2] P121/a1 (14) | 2a, b, c | (1/2)x + (1/4), y, z; +((1/2), 0, 0) | 4e | 2a; 2c | 4e | 2b; 2d | 4e | 2 × 4e |
| [2] P121/c1 (14) | a, b, 2c | x, y, (1/2)z; +(0, 0, (1/2)) | 2a; 2c | 2b; 2d | 4e | 4e | 4e | 2 × 4e |
| [2] P121/c1 (14) | a, b, 2c | x, y, (1/2)z + (1/4); +(0, 0, (1/2)) | 4e | 4e | 2a; 2c | 2b; 2d | 4e | 2 × 4e |
| [2] P121/c1 (14) | a - c, b, 2c | x, y, (1/2)(x + z); +(0, 0, (1/2)) | 2a; 2c | 4e | 4e | 2b; 2d | 4e | 2 × 4e |
| [2] P121/c1 (14) | a - c, b, 2c | x, y, (1/2)(x + z) + (1/4); +(0, 0, (1/2)) | 4e | 2b; 2d | 2a; 2c | 4e | 4e | 2 × 4e |
| Enlarged unit cell, isomorphic | ||||||||
| [3] P121/m1 | a, 3b, c | x, (1/3)y, z; ±(0, (1/3), 0) | 2a; 4f | 2b; 4f | 2c; 4f | 2d; 4f | 2e; 4f | 3 × 4f |
| [p] P121/m1 | a, pb, c | x, (1/p)y, z; +(0, (u/p), 0) | 2a; ((p - 1)/2) × 4f | 2b; ((p - 1)/2) × 4f | 2c; ((p - 1)/2) × 4f | 2d; ((p - 1)/2) × 4f | 2e; ((p - 1)/2) × 4f | p × 4f |
| p = prime > 2; u = 1, . . ., p - 1 | ||||||||
| [2] P121/m1 | 2a, b, c | (1/2)x, y, z; +((1/2), 0, 0) | 2a; 2b | 4f | 2c; 2d | 4f | 2 × 2e | 2 × 4f |
| [2] P121/m1 | 2a, b, c | (1/2)x + (1/4), y, z; +((1/2), 0, 0) | 4f | 2a; 2b | 4f | 2c; 2d | 2 × 2e | 2 × 4f |
| [2] P121/m1 | a - c, b, a + c | (1/2)(x - z), y, (1/2)(x + z); +((1/2), 0, (1/2)) | 2a; 2d | 4f | 4f | 2b; 2c | 2 × 2e | 2 × 4f |
| or: | a - c, b, 2c | x, y, (1/2)(x + z); +(0, 0, (1/2)) | 2a; 2c | 4f | 4f | 2b; 2d | 2 × 2e | 2 × 4f |
| [2] P121/m1 | a - c, b, a + c | (1/2)(x - z) + (1/4), y, (1/2)(x + z) + (1/4); | 4f | 2a; 2d | 2b; 2c | 4f | 2 × 2e | 2 × 4f |
| +((1/2), 0, (1/2)) | ||||||||
| or: | a - c, b, 2c | x, y, (1/2)(x + z) + (1/4); | 4f | 2b; 2d | 2a; 2c | 4f | 2 × 2e | 2 × 4f |
| +(0, 0, (1/2)) | ||||||||
| [2] P121/m1 | a, b, 2c | x, y, (1/2)z; +(0, 0, (1/2)) | 2a; 2c | 2b; 2d | 4f | 4f | 2 × 2e | 2 × 4f |
| [2] P121/m1 | a, b, 2c | x, y, (1/2)z + (1/4); +(0, 0, (1/2)) | 4f | 4f | 2a; 2c | 2b; 2d | 2 × 2e | 2 × 4f |
| [3] P121/m1 | 3a, b, c | (1/3)x, y, z; ±((1/3), 0, 0) | 2a; 4f | 2b; 4f | 2c; 4f | 2d; 4f | 3 × 2e | 3 × 4f |
| [3] P121/m1 | 3a, b, -a + c | (1/3)(x + z), y, z; ±((1/3), 0, 0) | 2a; 4f | 2b; 4f | 2d; 4f | 2c; 4f | 3 × 2e | 3 × 4f |
| [3] P121/m1 | 3a, b, a + c | (1/3)(x - z), y, z; ±((1/3), 0, 0) | 2a; 4f | 2b; 4f | 2d; 4f | 2c; 4f | 3 × 2e | 3 × 4f |
| [3] P121/m1 | a, b, 3c | x, y, (1/3)z; ±(0, 0, (1/3)) | 2a; 4f | 2b; 4f | 2c; 4f | 2d; 4f | 3 × 2e | 3 × 4f |
| [p] P121/m1 | a, b, pc | x, y, (1/p)z; +(0, 0, (u/p)) | 2a; ((p - 1)/2) × 4f | 2b; ((p - 1)/2) × 4f | 2c; ((p - 1)/2) × 4f | 2d; ((p - 1)/2) × 4f | p × 2e | p × 4f |
| p = prime > 2; u = 1, . . ., p - 1 | ||||||||
| [p] P121/m1 | pa, b, qa + c | (1/p)(x - qz), y, z; +((u/p), 0, 0) | 2a; ((p - 1)/2) × 4f | 2b; ((p - 1)/2) × 4f | 2c(d*); | 2d(c*); | p × 2e | p × 4f |
| p = prime > 2; u = 1, . . ., p - 1; | ((p - 1)/2) × 4f | ((p - 1)/2) × 4f | ||||||
| -(1/2)(p - 1)≤ q ≤ (1/2)(p - 1) | ||||||||
| * q = 2n + 1 | ||||||||
| P 1 1 21/m | ||||||||
|
UNIQUE AXIS c |
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| Axes | Coordinates | Wyckoff positions | ||||||
| 2a | 2b | 2c | 2d | 2e | 4f | |||
| I Maximal translationengleiche subgroups | ||||||||
| [2] P11m | x, y, z + (1/4) | 2c | 2c | 2c | 2c | 1a; 1b | 2 × 2c | |
| [2] P1121 | 2a | 2a | 2a | 2a | 2a | 2 × 2a | ||
| [2] P-1 | 1a; 1b | 1c; 1g | 1d; 1f | 1e; 1h | 2i | 2 × 2i | ||
| II Maximal klassengleiche subgroups | ||||||||
| Enlarged unit cell, non-isomorphic | ||||||||
| [2] P1121/b | a, 2b, c | x, (1/2)y, z; +(0, (1/2), 0) | 2a; 2c | 4e | 2b; 2d | 4e | 4e | 2 × 4e |
| [2] P1121/b | a, 2b, c | x, (1/2)y + (1/4), z; +(0, (1/2), 0) | 4e | 2a; 2c | 4e | 2b; 2d | 4e | 2 × 4e |
| [2] P1121/a | 2a, b, c | (1/2)x, y, z; +((1/2), 0, 0) | 2a; 2c | 2b; 2d | 4e | 4e | 4e | 2 × 4e |
| [2] P1121/a | 2a, b, c | (1/2)x + (1/4), y, z; +((1/2), 0, 0) | 4e | 4e | 2a; 2c | 2b; 2d | 4e | 2 × 4e |
| [2] P1121/a | 2a, -a + b, c | (1/2)(x + y), y, z; +((1/2), 0, 0) | 2a; 2c | 4e | 4e | 2b; 2d | 4e | 2 × 4e |
| [2] P1121/a | 2a, -a + b, c | (1/2)(x + y) + (1/4), y, z; +((1/2), 0, 0) | 4e | 2b; 2d | 2a; 2c | 4e | 4e | 2 × 4e |
| Enlarged unit cell, isomorphic | ||||||||
| [3] P1121/m | a, b, 3c | x, y, (1/3)z; ±(0, 0, (1/3)) | 2a; 4f | 2b; 4f | 2c; 4f | 2d; 4f | 2e; 4f | 3 × 4f |
| [p] P1121/m | a, b, pc | x, y, (1/p)z; +(0, 0, (u/p)) | 2a; ((p - 1)/2) × 4f | 2b; ((p - 1)/2) × 4f | 2c; ((p - 1)/2) × 4f | 2d; ((p - 1)/2) × 4f | 2e; ((p - 1)/2) × 4f | p × 4f |
| p = prime > 2; u = 1, . . ., p - 1 | ||||||||
| [2] P1121/m | a, 2b, c | x, (1/2)y, z; +(0, (1/2), 0) | 2a; 2b | 4f | 2c; 2d | 4f | 2 × 2e | 2 × 4f |
| [2] P1121/m | a, 2b, c | x, (1/2)y + (1/4), z; +(0, (1/2), 0) | 4f | 2a; 2b | 4f | 2c; 2d | 2 × 2e | 2 × 4f |
| [2] P1121/m | a + b, -a + b, c | (1/2)(x + y), (1/2)(-x + y), z; +((1/2), (1/2), 0) | 2a; 2d | 4f | 4f | 2b; 2c | 2 × 2e | 2 × 4f |
| or: | 2a, -a + b, c | (1/2)(x + y), y, z; +((1/2), 0, 0) | 2a; 2c | 4f | 4f | 2b; 2d | 2 × 2e | 2 × 4f |
| [2] P1121/m | a + b, -a + b, c | (1/2)(x + y) + (1/4), (1/2)(-x + y) + (1/4), z; +((1/2), (1/2), 0) | 4f | 2a; 2d | 2b; 2c | 4f | 2 × 2e | 2 × 4f |
| or: | 2a, -a + b, c | (1/2)(x + y) + (1/4), y, z; +((1/2), 0, 0) | 4f | 2b; 2d | 2a; 2c | 4f | 2 × 2e | 2 × 4f |
| [2] P1121/m | 2a, b, c | (1/2)x, y, z; +((1/2), 0, 0) | 2a; 2c | 2b; 2d | 4f | 4f | 2 × 2e | 2 × 4f |
| [2] P1121/m | 2a, b, c | (1/2)x + (1/4), y, z; +((1/2), 0, 0) | 4f | 4f | 2a; 2c | 2b; 2d | 2 × 2e | 2 × 4f |
| [3] P1121/m | a, 3b, c | x, (1/3)y, z; ±(0, (1/3), 0) | 2a; 4f | 2b; 4f | 2c; 4f | 2d; 4f | 3 × 2e | 3 × 4f |
| [3] P1121/m | a - b, 3b, c | x, (1/3)(x + y), z; ±(0, (1/3), 0) | 2a; 4f | 2b; 4f | 2d; 4f | 2c; 4f | 3 × 2e | 3 × 4f |
| [3] P1121/m | a + b, 3b, c | x, (1/3)(-x + y), z; ±(0, (1/3), 0) | 2a; 4f | 2b; 4f | 2d; 4f | 2c; 4f | 3 × 2e | 3 × 4f |
| [3] P1121/m | 3a, b, c | (1/3)x, y, z; ±((1/3), 0, 0) | 2a; 4f | 2b; 4f | 2c; 4f | 2d; 4f | 3 × 2e | 3 × 4f |
| [p] P1121/m | pa, b, c | (1/p)x, y, z; +((u/p), 0, 0) | 2a; ((p - 1)/2) × 4f | 2b; ((p - 1)/2) × 4f | 2c; ((p - 1)/2) × 4f | 2d; ((p - 1)/2) × 4f | p × 2e | p × 4f |
| p = prime > 2; u = 1, . . ., p - 1 | ||||||||
| [p] P1121/m | a + qb, pb, c | x, (1/p)(-qx + y), z; +(0, (u/p), 0) | 2a; ((p - 1)/2) × 4f | 2b; ((p - 1)/2) × 4f | 2c(d*); | 2d(c*); | p × 2e | p × 4f |
| p = prime > 2; u = 1, . . ., p - 1; | ((p - 1)/2) × 4f | ((p - 1)/2) × 4f | ||||||
| -(1/2)(p - 1)≤ q ≤ (1/2)(p - 1) | ||||||||
| * q = 2n + 1 | ||||||||
