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Axes |
Coordinates |
Wyckoff positions |
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4a |
4b |
8c |
8d |
8e |
8f |
16g |
| I Maximal translationengleiche subgroups |
| [2] I41 (80) |
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4a |
4a |
2 × 4a |
8b |
8b |
8b |
2 × 8b |
| [2] I212121(24) |
x, y + (1/4), z + (1/8) |
4c |
4c |
2 × 4c |
8d |
8d |
4a; 4b |
2 × 8d |
| [2] F222 |
a - b, |
(1/2)(x - y), (1/2)(x + y), z |
4a; 4d |
4b; 4c |
8g; 8h |
8f; 8j |
8e; 8i |
16k |
2 × 16k |
| (22) |
a + b, c |
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| II Maximal klassengleiche subgroups |
| Loss of centring translations |
| [2] P43212 (96) |
x + (1/4), y - (1/4), z + (1/4) |
4a |
4a |
8b |
8b |
2 × 4a |
8b |
2 × 8b |
| [2] P4322 (95) |
|
x + (1/4), y + (1/4), z + (1/8) |
4c |
4c |
8d |
2 × 4c |
8d |
4a; 4b |
2 × 8d |
| [2] P41212 (92) |
x + (1/4), y + (1/4), z |
4a |
4a |
8b |
2 × 4a |
8b |
8b |
2 × 8b |
| [2] P4122 (91) |
|
x + (1/4), y - (1/4), z + (1/8) |
4c |
4c |
8d |
8d |
2 × 4c |
4a; 4b |
2 × 8d |
| Enlarged unit cell, isomorphic |
| [3] I4122 |
b, -a, 3c |
y, -x, (1/3)z; ±(0, 0, (1/3)) |
4a; 8c |
4b; 8c |
3 × 8c |
8e; 16g |
8d; 16g |
8f; 16g |
3 × 16g |
| [p] I4122 |
b, -a, pc |
y, -x, (1/p)z; +(0, 0, (u/p)) |
4a; ((p - 1)/2) × 8c |
4b; ((p - 1)/2) × 8c |
p × 8c |
8e; ((p - 1)/2) × 16g |
8d; ((p - 1)/2) × 16g |
8f; ((p - 1)/2) × 16g |
p × 16g |
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p = prime = 4n - 1; |
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u = 1, . . ., p - 1 |
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| [5] I4122 |
a, b, 5c |
x, y, (1/5)z; ±(0, 0, (1/5)); |
4a; 2 × 8c |
4b; 2 × 8c |
5 × 8c |
8d; 2 × 16g |
8e; 2 × 16g |
8f; 2 × 16g |
5 × 16g |
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±(0, 0, (2/5)) |
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| [p] I4122 |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
4a; ((p - 1)/2) × 8c |
4b; ((p - 1)/2) × 8c |
p × 8c |
8d; ((p - 1)/2) × 16g |
8e; ((p - 1)/2) × 16g |
8f; ((p - 1)/2) × 16g |
p × 16g |
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p = prime = 4n + 1; |
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u = 1, . . ., p - 1 |
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| [9] I4122 |
3a, 3b, c |
(1/3)x, (1/3)y, z; |
4a; 8d; 8e; 16g |
4b; 8d; 8e; 16g |
8c; 4 × 16g |
3 × 8d; 3 × 16g |
3 × 8e; 3 × 16g |
3 × 8f; 3 × 16g |
9 × 16g |
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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] I4122 |
pa, pb, c |
(1/p)x, (1/p)y, z; |
4a; ((p - 1)/2) × 8d; |
4b; ((p - 1)/2) × 8d; |
8c; |
p × 8d; |
p × 8e; |
p × 8f; |
p2 × 16g |
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+((u/p), (v/p), 0) |
((p - 1)/2) × 8e; |
((p - 1)/2) × 8e; |
((p2 - 1)/2) × 16g |
((p(p - 1))/2) × 16g |
((p(p - 1))/2) × 16g |
((p(p - 1))/2) × 16g |
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p = prime > 2; |
(((p - 1)2)/4) × 16g |
(((p - 1)2)/4) × 16g |
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u, v = 1, . . ., p - 1 |
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