|
Axes |
Coordinates |
Wyckoff positions |
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2a |
2b |
4c |
4d |
4e |
8f |
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8g |
8h |
16i |
| I Maximal translationengleiche subgroups |
| [2] I-4 (82) |
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2a |
2b |
4f |
2c; 2d |
4e |
8g |
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2 × 4f |
8g |
2 × 8g |
| [2] I4 (79) |
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2a |
2a |
4b |
4b |
2 × 2a |
8c |
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2 × 4b |
8c |
2 × 8c |
| [2] I112/m (12) |
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2a |
2b |
2c; 2d |
4h |
4g |
4e; 4f |
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2 × 4h |
2 × 4i |
2 × 8j |
| II Maximal klassengleiche subgroups |
| Loss of centring translations |
| [2] P42/n (86) |
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origin 1: x, y, z |
2a |
2b |
4e |
4e |
4f |
4c; 4d |
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origin 2: x + (1/4), y + (1/4), z + (1/4) |
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2 × 4e |
8g |
2 × 8g |
| [2] P4/n (85) |
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origin 1: x + (1/2), y, z + (1/4) |
2c |
2c |
4f |
2a; 2b |
2 × 2c |
4d; 4e |
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origin 2: x + (1/4), y + (1/4), z + (1/4) |
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2 × 4f |
8g |
2 × 8g |
| [2] P42/m (84) |
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x + (1/2), y, z |
2d |
2c |
2a; 2b |
2e; 2f |
4i |
8k |
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4g; 4h |
2 × 4j |
2 × 8k |
| [2] P4/m (83) |
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1a; 1d |
1b; 1c |
2e; 2f |
4i |
2g; 2h |
8l |
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2 × 4i |
4j; 4k |
2 × 8l |
| Enlarged unit cell, isomorphic |
| [3] I4/m |
a, b, 3c |
x, y, (1/3)z; ±(0, 0, (1/3)) |
2a; 4e |
2b; 4e |
4c; 8g |
4d; 8g |
3 × 4e |
8f; 16i |
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3 × 8g |
8h; 16i |
3 × 16i |
| [p] I4/m |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
2a; ((p - 1)/2) × 4e |
2b; ((p - 1)/2) × 4e |
4c; ((p - 1)/2) × 8g |
4d; ((p - 1)/2) × 8g |
p × 4e |
8f; ((p - 1)/2) × 16i |
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p = prime > 2; u = 1, . . ., p - 1 |
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p × 8g |
8h; ((p - 1)/2) × 16i |
p × 16i |
| [5] I4/m |
a + 2b, |
(1/5)(x + 2y), (1/5)(-2x + y), z; |
2a; 8h |
2b; 8h |
4c; 2 × 8h |
4d; 16i |
4e; 16i |
8f; 2 × 16i |
|
-2a + b, c |
±((1/5), (3/5), 0); ±((2/5), (1/5), 0) |
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8g; 2 × 16i |
5 × 8h |
5 × 16i |
| [5] I4/m |
a - 2b, |
(1/5)(x - 2y), (1/5)(2x + y), z; |
2a; 8h |
2b; 8h |
4c; 2 × 8h |
4d; 16i |
4e; 16i |
8f; 2 × 16i |
|
2a + b, c |
±((1/5), (2/5), 0); ±((3/5), (1/5), 0) |
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8g; 2 × 16i |
5 × 8h |
5 × 16i |
| [p] I4/m |
qa - rb, |
(1/p)(qx - ry), (1/p)(rx + qy), z; |
2a; ((p - 1)/4) × 8h |
2b; ((p - 1)/4) × 8h |
4c; ((p - 1)/2) × 8h |
4d; ((p - 1)/4) × 16i |
4e; ((p - 1)/4) × 16i |
8f; ((p - 1)/2) × 16i |
|
ra + qb, c |
+((uq/p), (ur/p), 0) |
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8g; ((p - 1)/2) × 16i |
p × 8h |
p × 16i |
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p = q2 + r2 = prime = 4n + 1; |
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q = 2n + 1 ≥ 1; r = ± 2n'≠ 0; |
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u = 1, . . ., p - 1 |
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| [9] I4/m |
3a, 3b, c |
(1/3)x, (1/3)y, z; |
2a; 2 × 8h |
2b; 2 × 8h |
4c; 4 × 8h |
4d; 2 × 16i |
4e; 2 × 16i |
8f; 4 × 16i |
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±((1/3), 0, 0); ±(0, (1/3), 0); |
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8g; 4 × 16i |
9 × 8h |
9 × 16i |
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±((1/3), (1/3), 0); ±((1/3), (2/3), 0) |
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| [p2] I4/m |
pa, pb, c |
(1/p)x, (1/p)y, z; +((u/p), (v/p), 0) |
2a; ((p2 - 1)/4) × 8h |
2b; ((p2 - 1)/4) × 8h |
4c; ((p2 - 1)/2) × 8h |
4d; ((p2 - 1)/4) × 16i |
4e; ((p2 - 1)/4) × 16i |
8f; ((p2 - 1)/2) × 16i |
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p = prime = 4n - 1; |
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8g; ((p2 - 1)/2) × 16i |
p2 × 8h |
p2 × 16i |
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u, v = 1, . . ., p - 1 |
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