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Axes |
Coordinates |
Wyckoff positions |
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1a |
1b |
1c |
3d |
6e |
| I Maximal translationengleiche subgroups |
| [2] P3 (143) |
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1a |
1b |
1c |
3d |
2 × 3d |
| [3] C1m1 (8) |
2a + b, b, c |
(1/2)x, -(1/2)x + y, z |
2a |
2a |
2a |
2a; 4b |
3 × 4b |
| 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 |
| [2] P3c1 |
a, b, 2c |
x, y, (1/2)z; +(0, 0, (1/2)) |
2a |
2b |
2c |
6d |
2 × 6d |
| (158) |
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| [3] P31m |
2a + b, -a + b, c |
(1/3)(x + y), (1/3)(-x + 2y), z; |
1a; 2b |
3c |
3c |
3c; 6d |
3 × 6d |
| (157) |
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±((2/3), (1/3), 0) |
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| [3] P31m |
2a + b, -a + b, c |
(1/3)(x + y) + (1/3), (1/3)(-x + 2y), z; |
3c |
1a; 2b |
3c |
3c; 6d |
3 × 6d |
| (157) |
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±((2/3), (1/3), 0) |
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| [3] P31m |
2a + b, -a + b, c |
(1/3)(x + y) - (1/3), (1/3)(-x + 2y), z; |
3c |
3c |
1a; 2b |
3c; 6d |
3 × 6d |
| (157) |
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±((2/3), (1/3), 0) |
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| Enlarged unit cell, isomorphic |
| [2] P3m1 |
a, b, 2c |
x, y, (1/2)z; +(0, 0, (1/2)) |
2 × 1a |
2 × 1b |
2 × 1c |
2 × 3d |
2 × 6e |
| [3] P3m1 |
a, b, 3c |
x, y, (1/3)z; ±(0, 0, (1/3)) |
3 × 1a |
3 × 1b |
3 × 1c |
3 × 3d |
3 × 6e |
| [p] P3m1 |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
p × 1a |
p × 1b |
p × 1c |
p × 3d |
p × 6e |
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p = prime; u = 1, . . ., p - 1 |
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| [4] P3m1 |
2a, 2b, c |
(1/2)x, (1/2)y, z; +((1/2), 0, 0); |
1a; 3d |
1c; 3d |
1b; 3d |
2 × 3d; 6e |
4 × 6e |
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+(0, (1/2), 0); +((1/2), (1/2), 0) |
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| [p2] P3m1 |
pa, pb, c |
(1/p)x, (1/p)y, z; +((u/p), (v/p), 0) |
1a; (p - 1) × 3d; |
1b(c*); |
1c(b*); |
p × 3d; |
p2 × 6e |
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p = prime ≠ 3; u, v = 1, . . ., p - 1 |
(((p - 1)(p - 2))/6) × 6e |
(p - 1) × 3d; |
(p - 1) × 3d; |
((p(p - 1))/2) × 6e |
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(((p - 1)(p - 2))/6) × 6e |
(((p - 1)(p - 2))/6) × 6e |
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| * p = 3n - 1 |
