|
Axes |
Coordinates |
Wyckoff positions |
|
|
|
4a |
4b |
8c |
8d |
16e |
| I Maximal translationengleiche subgroups |
| [2] I-4 (82) |
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|
2a; 2c |
2b; 2d |
4e; 4f |
8g |
2 × 8g |
| [2] I212121 (24) |
|
x, y + (1/4), z + (1/8) |
4c |
4c |
2 × 4c |
4a; 4b |
2 × 8d |
| [2] Fdd2 (43) |
a + b, -a + b, c |
(1/2)(x + y), (1/2)(-x + y), z |
8a |
8a |
2 × 8a |
16b |
2 × 16b |
| II Maximal klassengleiche subgroups |
| Enlarged unit cell, isomorphic |
| [3] I-42d |
b, -a, 3c |
y, -x, (1/3)z; ±(0, 0, (1/3)) |
4a; 8c |
4b; 8c |
3 × 8c |
8d; 16e |
3 × 16e |
| [p] I-42d |
b, -a, pc |
y, -x, (1/p)z; +(0, 0, (u/p)) |
4a; ((p - 1)/2) × 8c |
4b; ((p - 1)/2) × 8c |
p × 8c |
8d; ((p - 1)/2) × 16e |
p × 16e |
|
p = prime = 4n - 1; u = 1, . . ., p - 1 |
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| [5] I-42d |
a, b, 5c |
x, y, (1/5)z; ±(0, 0, (1/5)); ±(0, 0, (2/5)) |
4a; 2 × 8c |
4b; 2 × 8c |
5 × 8c |
8d; 2 × 16e |
5 × 16e |
| [p] I-42d |
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) × 16e |
p × 16e |
|
p = prime = 4n + 1; u = 1, . . ., p - 1 |
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| [9] I-42d |
3a, 3b, c |
(1/3)x, (1/3)y, z; ±((1/3), 0, 0); ±(0, (1/3), 0); |
4a; 2 × 16e |
4b; 2 × 16e |
8c; 4 × 16e |
3 × 8d; 3 × 16e |
9 × 16e |
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±((1/3), (1/3), 0); ±((1/3), (2/3), 0) |
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| [p2] I-42d |
pa, pb, c |
(1/p)x, (1/p)y, z; +((u/p), (v/p), 0) |
4a; ((p2 - 1)/4) × 16e |
4b; ((p2 - 1)/4) × 16e |
8c; ((p2 - 1)/2) × 16e |
p × 8d; |
p2 × 16e |
|
p = prime > 2; u, v = 1, . . ., p - 1 |
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((p(p - 1))/2) × 16e |
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