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Axes |
Coordinates |
Wyckoff positions |
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2a |
2b |
4c |
4d |
6e |
6f |
12g |
| I Maximal translationengleiche subgroups |
| [2] P3c1 (158) |
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2a |
2a |
2 × 2a |
2b; 2c |
6d |
6d |
2 × 6d |
| [2] P321 (150) |
x, y, z + (1/4) |
1a; 1b |
2c |
2 × 2c |
2 × 2d |
6g |
3e; 3f |
2 × 6g |
| [2] P-3 (147) |
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2c |
1a; 1b |
2 × 2c |
2 × 2d |
3e; 3f |
6g |
2 × 6g |
| [3] C12/c1 |
2a + b, b, c |
(1/2)x, -(1/2)x + y, z |
4e |
4a |
8f |
8f |
4b; 4c; 4d |
4e; 8f |
3 × 8f |
| (15) |
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| conjugate: |
a - b, a + b, c |
(1/2)(x - y), (1/2)(x + y), z |
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| conjugate: |
a + 2b, -a, c |
(1/2)y, -x + (1/2)y, z |
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| II Maximal klassengleiche subgroups |
| Enlarged unit cell, non-isomorphic |
| [3] P-31c |
2a + b, |
(1/3)(x + y), (1/3)(-x + 2y), z; |
2a; 2c; 2d |
2b; 4f |
4e; 2 × 4f |
12i |
6g; 12i |
3 × 6h |
3 × 12i |
| (163) |
-a + b, c |
±((2/3), (1/3), 0) |
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| Enlarged unit cell, isomorphic |
| [3] P-3c1 |
a, b, 3c |
x, y, (1/3)z; ±(0, 0, (1/3)) |
2a; 4c |
2b; 4c |
3 × 4c |
3 × 4d |
6e; 12g |
6f; 12g |
3 × 12g |
| [p] P-3c1 |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
2a; ((p - 1)/2) × 4c |
2b; ((p - 1)/2) × 4c |
p × 4c |
p × 4d |
6e; ((p - 1)/2) × 12g |
6f; ((p - 1)/2) × 12g |
p × 12g |
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p = prime > 2; u = 1, . . ., p - 1 |
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| [4] P-3c1 |
2a, 2b, c |
(1/2)x, (1/2)y, z; +((1/2), 0, 0); |
2a; 6f |
2b; 6e |
4c; 12g |
4d; 12g |
2 × 12g |
2 × 6f; 12g |
4 × 12g |
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+(0, (1/2), 0); +((1/2), (1/2), 0) |
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| [p2] P-3c1 |
pa, pb, c |
(1/p)x, (1/p)y, z; +((u/p), (v/p), 0) |
2a; (p - 1) × 6f; |
2b; ((p2 - 1)/6) × |
4c; |
4d; |
6e; ((p2 - 1)/2) × 12g |
p × 6f; |
p2 × 12g |
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p = prime > 4; |
(((p - 1)(p - 2))/6) × 12g |
12g |
((p2 - 1)/3) × 12g |
((p2 - 1)/3) × 12g |
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((p(p - 1))/2) × 12g |
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u, v = 1, . . ., p - 1 |
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