| R3c | No. 161 | C3v6 |
HEXAGONAL AXES
| Axes | Coordinates | Wyckoff positions | |||
| 6a | 18b | ||||
| I Maximal translationengleiche subgroups | |||||
| [2] R3 (146) | 2 × 3a | 2 × 9b | |||
| [3] C1c1 (9) | (1/3)(2a + b - 2c), b, c | (3/2)x, -(1/2)x + y, x + z | 4a | 3 × 4a | |
| conjugate: | (1/3)(-a + b - 2c), -a - b, c | (3/2)(-x + y), -(1/2)(x + y), -x + y + z | |||
| conjugate: | (1/3)(-a - 2b - 2c), a, c | -(3/2)y, x - (1/2)y, -y + z | |||
| alternative: | 2a + b, b, -(2/3)(2a + b) + (1/3)c | (1/2)x + 2z, -(1/2)x + y, 3z | |||
| or | -a + b, -a - b, (2/3)(a - b) + (1/3)c | (1/2)(-x + y) + 2z, -(1/2)(x + y), 3z | |||
| or | -a - 2b, a, (2/3)(a + 2b) + (1/3)c | -(1/2)y + 2z, x - (1/2)y, 3z | |||
| II Maximal klassengleiche subgroups | |||||
| Loss of centring translations | |||||
| [3] P3c1 (158) | 2a; 2b; 2c | 3 × 6d | |||
| Enlarged unit cell, isomorphic | |||||
| [5] R3c | -a, -b, 5c | -x, -y, (1/5)z; ±(0, 0, (1/5)); ±(0, 0, (2/5)) | 5 × 6a | 5 × 18b | |
| [p] R3c | -a, -b, pc | -x, -y, (1/p)z; +(0, 0, (u/p)) | p × 6a | p × 18b | |
| p = prime = 6n - 1; u = 1, . . ., p - 1 | |||||
| a, b, pc | x, y, (1/p)z; +(0, 0, (u/p)) | ||||
| p = prime = 6n + 1; u = 1, . . ., p - 1 | |||||
| [4] R3c | -2a, -2b, c | -(1/2)x, -(1/2)y, z; +((1/2), 0, 0); (0, (1/2), 0); | 6a; 18b | 4 × 18b | |
| +((1/2), (1/2), 0) | |||||
| [p2] R3c | -pa, -pb, c | -(1/p)x, -(1/p)y, z; +((u/p), (v/p), 0) | 6a; ((p2 - 1)/3) × 18b | p2 × 18b | |
| p = prime = 3n - 1; u, v = 1, . . ., p - 1 | |||||
| pa, pb, c | (1/p)x, (1/p)y, z +((u/p), (v/p), 0) | ||||
| p = prime = 6n + 1; u, v = 1, . . ., p - 1 | |||||
