|
Axes |
Coordinates |
Wyckoff positions |
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2a |
2b |
2c |
2d |
4e |
4f |
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4g |
4h |
4i |
8j |
| I Maximal translationengleiche subgroups |
| [2] P-4 |
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2e |
2f |
1a; 1b |
1c; 1d |
4h |
4h |
| (81) |
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2 × 2e |
2 × 2f |
2 × 2g |
2 × 4h |
| [2] Pcc2 |
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2a |
2d |
2a |
2d |
4e |
4e |
| (27) |
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2 × 2a |
2 × 2d |
2b; 2c |
2 × 4e |
| [2] C222 |
a - b, |
(1/2)(x - y), (1/2)(x + y), z + (1/4) |
2a; 2d |
2b; 2c |
4i |
4j |
4e; 4h |
4f; 4g |
| (21) |
a + b, c |
|
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|
2 × 4i |
2 × 4j |
2 × 4k |
2 × 8l |
| II Maximal klassengleiche subgroups |
| Enlarged unit cell, non-isomorphic |
| [2] P-421c |
a - b, |
(1/2)(x - y), (1/2)(x + y), z; |
4c |
4d |
2a; 2b |
4d |
8e |
8e |
| (114) |
a + b, c |
+((1/2), (1/2), 0) |
|
|
2 × 4c |
2 × 4d |
8e |
2 × 8e |
| [2] P-421c |
a - b, |
(1/2)(x - y) + (1/2), (1/2)(x + y), z; |
4d |
4c |
4d |
2a; 2b |
8e |
8e |
| (114) |
a + b, c |
+((1/2), (1/2), 0) |
|
|
2 × 4d |
2 × 4c |
8e |
2 × 8e |
| [2] P-42c |
a - b, |
(1/2)(x - y), (1/2)(x + y), z; |
2a; 2c |
2b; 2d |
2e; 2f |
4m |
4h; 4j |
4g; 4i |
| (112) |
a + b, c |
+((1/2), (1/2), 0) |
|
|
4k; 4l |
2 × 4m |
8n |
2 × 8n |
| [2] P-42c |
a - b, |
(1/2)(x - y) + (1/2), (1/2)(x + y), z; |
2b; 2d |
2a; 2c |
4m |
2e; 2f |
4h; 4j |
4g; 4i |
| (112) |
a + b, c |
+((1/2), (1/2), 0) |
|
|
2 × 4m |
4k; 4l |
8n |
2 × 8n |
| Enlarged unit cell, isomorphic |
| [3] P-4c2 |
a, b, 3c |
x, y, (1/3)z; ±(0, 0, (1/3)) |
2a; 4g |
2b; 4h |
2c; 4g |
2d; 4h |
4f; 8j |
4e; 8j |
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|
3 × 4g |
3 × 4h |
3 × 4i |
3 × 8j |
| [p] P-4c2 |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
2a; ((p - 1)/2) × 4g |
2b; ((p - 1)/2) × 4h |
2c; ((p - 1)/2) × 4g |
2d; ((p - 1)/2) × 4h |
4e(f*); ((p - 1)/2) × 8j |
4f(e*); ((p - 1)/2) × 8j |
|
p = prime > 2; |
|
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p × 4g |
p × 4h |
p × 4i |
p × 8j |
|
u = 1, . . ., p - 1 |
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| [9] P-4c2 |
3a, 3b, c |
(1/3)x, (1/3)y, z; |
2a; 4e; 4f; 8j |
2b; 4e; 4f; 8j |
2c; 2 × 8j |
2d; 2 × 8j |
3 × 4e; 3 × 8j |
3 × 4 f; 3 × 8j |
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±((1/3), 0, 0); ±(0, (1/3), 0); |
|
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4g; 4 × 8j |
4h; 4 × 8j |
4i; 4 × 8j |
9 × 8j |
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±((1/3), (1/3), 0); ±((1/3), (2/3), 0) |
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| [p2] P-4c2 |
pa, pb, c |
(1/p)x, (1/p)y, z; +((u/p), (v/p), 0) |
2a; ((p - 1)/2) × 4e; |
2b; ((p - 1)/2) × 4e; |
2c; ((p2 - 1)/4) × 8j |
2d; ((p2 - 1)/4) × 8j |
p × 4e; ((p(p - 1))/2) × 8j |
p × 4f; ((p(p - 1))/2) × 8j |
|
p = prime > 2; |
((p - 1)/2) × 4f; |
((p - 1)/2) × 4f; |
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u, v = 1, . . ., p - 1 |
(((p - 1)2)/4) × 8j |
(((p - 1)2)/4) × 8j |
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4g; ((p2 - 1)/2) × 8j |
4h; ((p2 - 1)/2) × 8j |
4i; ((p2 - 1)/2) × 8j |
p2 × 8j |
|
| * p = 4n - 1 |
