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Axes |
Coordinates |
Wyckoff positions |
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2a |
2b |
2c |
2d |
4e |
4f |
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4g |
4h |
8i |
| I Maximal translationengleiche subgroups |
| [2] P-4 (81) |
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1a; 1d |
1b; 1c |
2g |
2g |
2e; 2f |
4h |
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4h |
2 × 2g |
2 × 4h |
| [2] Pnn2 |
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2a |
2a |
2b |
2b |
2 × 2a |
4c |
| (34) |
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4c |
2 × 2b |
2 × 4c |
| [2] C222 |
a - b, |
(1/2)(x - y) + (1/4), |
4k |
4k |
2a; 2c |
2b; 2d |
2 × 4k |
4f; 4g |
| (21) |
a + b, c |
(1/2)(x + y) + (1/4), z + (1/4) |
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4e; 4h |
4i; 4j |
2 × 8l |
| II Maximal klassengleiche subgroups |
| Enlarged unit cell, non-isomorphic |
| [2] I-42d |
a - b, |
(1/2)(x - y), (1/2)(x + y), (1/2)z; |
4a; 4b |
8c |
8d |
8d |
2 × 8c |
2 × 8d |
| (122) |
a + b, 2c |
+(0, 0, (1/2)) |
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16e |
16e |
2 × 16e |
| [2] I-42d |
a - b, |
(1/2)(x - y), (1/2)(x + y), |
8c |
4a; 4b |
8d |
8d |
2 × 8c |
16e |
| (122) |
a + b, 2c |
(1/2)z + (1/4); +(0, 0, (1/2)) |
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2 × 8d |
16e |
2 × 16e |
| [2] I-42d |
a - b, |
(1/2)(x - y) + (1/2), (1/2)(x + y), (1/2)z; |
8c |
4a; 4b |
8d |
8d |
2 × 8c |
2 × 8d |
| (122) |
a + b, 2c |
+(0, 0, (1/2)) |
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16e |
16e |
2 × 16e |
| [2] I-42d |
a - b, |
(1/2)(x - y) + (1/2), (1/2)(x + y), |
4a; 4b |
8c |
8d |
8d |
2 × 8c |
16e |
| (122) |
a + b, 2c |
(1/2)z + (1/4); +(0, 0, (1/2)) |
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2 × 8d |
16e |
2 × 16e |
| Enlarged unit cell, isomorphic |
| [3] P-4n2 |
a, b, 3c |
x, y, (1/3)z; |
2a; 4e |
2b; 4e |
2d; 4h |
2c; 4h |
3 × 4e |
4g; 8i |
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±(0, 0, (1/3)) |
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4f; 8i |
3 × 4h |
3 × 8i |
| [p] P-4n2 |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
2a; ((p - 1)/2) × 4e |
2b; ((p - 1)/2) × 4e |
2c(d*); ((p - 1)/2) × 4h |
2d(c*); ((p - 1)/2) × 4h |
p × 4e |
4f(g*); ((p - 1)/2) × 8i |
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p = prime > 2; |
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4g(f*); ((p - 1)/2) × 8i |
p × 4h |
p × 8i |
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u = 1, . . ., p - 1 |
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| [9] P-4n2 |
3a, 3b, c |
(1/3)x, (1/3)y, z; |
2a; 2 × 8i |
2b; 2 × 8i |
2c; 4f; 4g; 8i |
2d; 4f; 4g; 8i |
4e; 4 × 8i |
3 × 4f; 3 × 8i |
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±((1/3), 0, 0); ±(0, (1/3), 0); |
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3 × 4g; 3 × 8i |
4h; 4 × 8i |
9 × 8i |
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±((1/3), (1/3), 0); ±((1/3), (2/3), 0) |
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| [p2] P-4n2 |
pa, pb, c |
(1/p)x, (1/p)y, z; +((u/p), (v/p), 0) |
2a; ((p2 - 1)/4) × 8i |
2b; ((p2 - 1)/4) × 8i |
2c; ((p - 1)/2) × 4f; |
2d; ((p - 1)/2) × 4f; |
4e; ((p2 - 1)/2) × 8i |
p × 4f; ((p(p - 1))/2) × 8i |
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p = prime > 2; |
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((p - 1)/2) × 4g; |
((p - 1)/2) × 4g; |
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u, v = 1, . . ., p - 1 |
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(((p - 1)2)/4) × 8i |
(((p - 1)2)/4) × 8i |
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p × 4g; ((p(p - 1))/2) × 8i |
4h; ((p2 - 1)/2) × 8i |
p2 × 8i |
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| * p = 4n - 1 |
