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Axes |
Coordinates |
Wyckoff positions |
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1a |
1b |
2c |
2d |
3e |
3f |
6g |
| I Maximal translationengleiche subgroups |
| [2] P3 (143) |
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1a |
1a |
2 × 1a |
1b; 1c |
3d |
3d |
2 × 3d |
| [3] C121 |
2a + b, |
(1/2)x, -(1/2)x + y, z; |
2a |
2b |
4c |
4c |
2a; 4c |
2b; 4c |
3 × 4c |
| (5) |
b, c |
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| conjugate: |
a - b, |
(1/2)(x - y), (1/2)(x + y), z; |
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a + b, c |
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| conjugate: |
a + 2b, |
(1/2)y, -x + (1/2)y, z; |
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-a, c |
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| II Maximal klassengleiche subgroups |
| Enlarged unit cell, non-isomorphic |
| [3] P3221 |
a, b, 3c |
x, y, (1/3)z; ±(0, 0, (1/3)) |
3a |
3b |
6c |
6c |
3a; 6c |
3b; 6c |
3 × 6c |
| (154) |
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| [3] P3121 |
a, b, 3c |
x, y, (1/3)z; ±(0, 0, (1/3)) |
3a |
3b |
6c |
6c |
3a; 6c |
3b; 6c |
3 × 6c |
| (152) |
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| [3] P312 |
2a + b, |
(1/3)(x + y), (1/3)(-x + 2y), z; |
1a; 1c; 1e |
1b; 1d; 1f |
2g; 2h; 2i |
6l |
3 × 3j |
3 × 3k |
3 × 6l |
| (149) |
-a + b, c |
±((2/3), (1/3), 0) |
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| Enlarged unit cell, isomorphic |
| [2] P321 |
a, b, 2c |
x, y, (1/2)z; +(0, 0, (1/2)) |
1a; 1b |
2c |
2 × 2c |
2 × 2d |
3e; 3f |
6g |
2 × 6g |
| [2] P321 |
a, b, 2c |
x, y, (1/2)z + (1/4); +(0, 0, (1/2)) |
2c |
1a; 1b |
2 × 2c |
2 × 2d |
6g |
3e; 3f |
2 × 6g |
| [3] P321 |
a, b, 3c |
x, y, (1/3)z; ±(0, 0, (1/3)) |
1a; 2c |
1b; 2c |
3 × 2c |
3 × 2d |
3e; 6g |
3f; 6g |
3 × 6g |
| [p] P321 |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
1a; ((p - 1)/2) × 2c |
1b; ((p - 1)/2) × 2c |
p × 2c |
p × 2d |
3e; ((p - 1)/2) × 6g |
3f; ((p - 1)/2) × 6g |
p × 6g |
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p = prime > 2; u = 1, . . ., p - 1 |
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| [4] P321 |
2a, 2b, c |
(1/2)x, (1/2)y, z; +((1/2), 0, 0); |
1a; 3e |
1b; 3f |
2c; 6g |
2d; 6g |
2 × 3e; 6g |
2 × 3f; 6g |
4 × 6g |
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+(0, (1/2), 0); +((1/2), (1/2), 0) |
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| [p2] P321 |
pa, pb, c |
(1/p)x, (1/p)y, z; +((u/p), (v/p), 0) |
1a; (p - 1) × 3e; |
1b; (p - 1) × 3f; |
2c; ((p2 - 1)/3) × 6g |
2d; ((p2 - 1)/3) × 6g |
p × 3e; |
p × 3f; |
p2 × 6g |
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p = prime ≠ 3; |
(((p - 1)(p - 2))/6) × 6g |
(((p - 1)(p - 2))/6) × 6g |
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((p(p - 1))/2) × 6g |
((p(p - 1))/2) × 6g |
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u, v = 1, . . ., p - 1 |
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