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Axes |
Coordinates |
Wyckoff positions |
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2a |
2b |
2c |
4d |
4e |
4f |
8g |
| I Maximal translationengleiche subgroups |
| [2] P4 (75) |
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x + (1/2), y, z |
2c |
2c |
1a; 1b |
2 × 2c |
4d |
4d |
2 × 4d |
| [2] P21212 |
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2a |
2a |
2b |
2 × 2a |
4c |
4c |
2 × 4c |
| (18) |
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| [2] C222 |
a - b, |
(1/2)(x - y), (1/2)(x + y), z |
2a; 2b |
2c; 2d |
4k |
4i; 4j |
4e; 4g |
4f; 4h |
2 × 8l |
| (21) |
a + b, c |
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| II Maximal klassengleiche subgroups |
| Enlarged unit cell, non-isomorphic |
| [2] P42212 |
a, b, 2c |
x, y, (1/2)z; +(0, 0, (1/2)) |
2a; 2b |
4c |
4d |
2 × 4c |
4e; 4f |
8g |
2 × 8g |
| (94) |
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| [2] P42212 |
a, b, 2c |
x, y, (1/2)z + (1/4); +(0, 0, (1/2)) |
4c |
2a; 2b |
4d |
2 × 4c |
8g |
4e; 4f |
2 × 8g |
| (94) |
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| Enlarged unit cell, isomorphic |
| [2] P4212 |
a, b, 2c |
x, y, (1/2)z; +(0, 0, (1/2)) |
2a; 2b |
4d |
2 × 2c |
2 × 4d |
4e; 4f |
8g |
2 × 8g |
| [2] P4212 |
a, b, 2c |
x, y, (1/2)z + (1/4); +(0, 0, (1/2)) |
4d |
2a; 2b |
2 × 2c |
2 × 4d |
8g |
4e; 4f |
2 × 8g |
| [3] P4212 |
a, b, 3c |
x, y, (1/3)z; ±(0, 0, (1/3)) |
2a; 4d |
2b; 4d |
3 × 2c |
3 × 4d |
4e; 8g |
4f; 8g |
3 × 8g |
| [p] P4212 |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
2a; ((p - 1)/2) × 4d |
2b; ((p - 1)/2) × 4d |
p × 2c |
p × 4d |
4e; ((p - 1)/2) × 8g |
4f; ((p - 1)/2) × 8g |
p × 8g |
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p = prime > 2 |
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u = 1, . . ., p - 1 |
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| [9] P4212 |
3a, 3b, c |
(1/3)x, (1/3)y, z; |
2a; 2 × 4e; 8g |
2b; 2 × 4f; 8g |
2c; 2 × 8g |
4d; 4 × 8g |
3 × 4e; 3 × 8g |
3 × 4f; 3 × 8g |
9 × 8g |
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±((1/3), 0, 0); ±(0, (1/3), 0); |
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±((1/3), (1/3), 0); ±((1/3), (2/3), 0) |
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| [p2] P4212 |
pa, pb, c |
(1/p)x, (1/p)y, z; +((u/p), (v/p), 0) |
2a; (p - 1) × 4e; |
2b; (p - 1) × 4f; |
2c; |
4d; |
p × 4e; |
p × 4f; |
p2 × 8g |
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p = prime > 2; |
(((p - 1)2)/4) × 8g |
(((p - 1)2)/4) × 8g |
((p2 - 1)/4) × 8g |
((p2 - 1)/2) × 8g |
((p(p - 1))/2) × 8g |
((p(p - 1))/2) × 8g |
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u, v = 1, . . ., p - 1 |
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