|
Axes |
Coordinates |
Wyckoff positions |
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1a |
2b |
3c |
6d |
| I Maximal translationengleiche subgroups |
| [2] P3 (143) |
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|
1a |
1b; 1c |
3d |
2 × 3d |
| [3] C1m1 (8) |
a, a + 2b, c |
x - (1/2)y, (1/2)y, z |
2a |
4b |
2a; 4b |
3 × 4b |
| conjugate: |
b, -2a - b, c |
-(1/2)x + y, -(1/2)x, z |
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| conjugate: |
a + b, -a + b, c |
(1/2)(x + y), (1/2)(-x + y), z |
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| II Maximal klassengleiche subgroups |
| Enlarged unit cell, non-isomorphic |
| [3] R3m (160) |
a - b, a + 2b, 3c |
(1/3)(2x - y), (1/3)(x + y), (1/3)z; ±(0, 0, (1/3)) |
3 × 3a |
18c |
3 × 9b |
3 × 18c |
|
(hexagonal axes) |
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| [3] R3m (160) |
2a + b, -a + b, 3c |
(1/3)(x + y), (1/3)(-x + 2y), (1/3)z; ±(0, 0, (1/3)) |
3 × 3a |
18c |
3 × 9b |
3 × 18c |
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(hexagonal axes) |
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| [2] P31c (159) |
a, b, 2c |
x, y, (1/2)z; +(0, 0, (1/2)) |
2a |
2 × 2b |
6c |
2 × 6c |
| [3] P3m1 (156) |
a - b, a + 2b, c |
(1/3)(2x - y), (1/3)(x + y), z; ±((2/3), (1/3), 0) |
1a; 1b; 1c |
6e |
3 × 3d |
3 × 6e |
| Enlarged unit cell, isomorphic |
| [2] P31m |
a, b, 2c |
x, y, (1/2)z; +(0, 0, (1/2)) |
2 × 1a |
2 × 2b |
2 × 3c |
2 × 6d |
| [3] P31m |
a, b, 3c |
x, y, (1/3)z; ±(0, 0, (1/3)) |
3 × 1a |
3 × 2b |
3 × 3c |
3 × 6d |
| [p] P31m |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
p × 1a |
p × 2b |
p × 3c |
p × 6d |
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p = prime; u = 1, . . ., p - 1 |
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| [4] P31m |
2a, 2b, c |
(1/2)x, (1/2)y, z; +((1/2), 0, 0); +(0, (1/2), 0); +((1/2), (1/2), 0) |
1a; 3c |
2b; 6d |
2 × 3c; 6d |
4 × 6d |
| [p2] P31m |
pa, pb, c |
(1/p)x, (1/p)y, z; +((u/p), (v/p), 0) |
1a; (p - 1) × 3c; |
2b; ((p2 - 1)/3) × 6d |
p × 3c; |
p2 × 6d |
|
p = prime ≠ 3; u, v = 1, . . ., p - 1 |
(((p - 1)(p - 2))/6) × 6d |
|
((p(p - 1))/2) × 6d |
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