|
Axes |
Coordinates |
Wyckoff positions |
|
|
origin 1 |
origin 2 |
4a |
4b |
8c |
8d |
8e |
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|
|
16f |
16g |
16h |
32i |
| I Maximal translationengleiche subgroups |
| [2] I-42d |
|
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x, y - (1/4), z + (1/8) |
4a |
4b |
8d |
8d |
8c |
| (122) |
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|
|
2 × 8d |
16e |
16e |
2 × 16e |
| [2] I-4m2 |
|
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x, y - (1/4), z + (1/8) |
2a; 2c |
2b; 2d |
8i |
8i |
4e; 4f |
| (119) |
|
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|
16j |
8g; 8h |
2 × 8i |
2 × 16j |
| [2] I41md |
|
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x, y - (1/4), z |
4a |
4a |
8b |
8b |
2 × 4a |
| (109) |
|
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|
|
16c |
16c |
2 × 8b |
2 × 16c |
| [2] I4122 |
|
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x, y - (1/4), z + (1/8) |
4a |
4b |
8f |
8f |
8c |
| (98) |
|
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|
|
2 × 8f |
8d; 8e |
16g |
2 × 16g |
| [2] I41/a |
|
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x, y + (1/2), z |
4a |
4b |
8c |
8d |
8e |
| (88) |
|
|
|
|
16f |
16f |
16f |
2 × 16f |
| [2] Imma |
|
x, y + (1/4), z - (1/8) |
|
4e |
4e |
4a; 4d |
4b; 4c |
2 × 4e |
| (74) |
|
|
|
|
8f; 8g |
16j |
8h; 8i |
2 × 16j |
| [2] Fddd |
a + b, |
(1/2)(x + y), |
(1/2)(x + y) + (1/4), |
8a |
8b |
16c |
16d |
16g |
| (70) |
-a + b, c |
(1/2)(-x + y), z |
(1/2)(-x + y) + (1/4), z |
|
32h |
16e; 16f |
32h |
2 × 32h |
| Enlarged unit cell, isomorphic |
| [3] I41/amd |
a, b, 3c |
x + (1/2), y, (1/3)z - (1/4); |
x + (1/2), y, (1/3)z; |
4a; 8e |
4b; 8e |
8d; 16h |
8c; 16h |
3 × 8e |
|
|
±(0, 0, (1/3)) |
±(0, 0, (1/3)) |
|
16f; 32i |
16g; 32i |
3 × 16h |
3 × 32i |
| [p] I41/amd |
a, b, pc |
x, y, (1/p)z; |
x, y, (1/p)z; |
4a(b*); ((p - 1)/2) × 8e |
4b(a*); ((p - 1)/2) × 8e |
8c(d† ); ((p - 1)/2) × 16h |
8d(c† ); ((p - 1)/2) × 16h |
p × 8e |
|
|
+(0, 0, (u/p)) |
+(0, 0, (u/p)) |
|
16f; ((p - 1)/2) × 32i |
16g; ((p - 1)/2) × 32i |
p × 16h |
p × 32i |
|
p = prime; = 4n + 1 u = 0, . . ., p - 1 |
|
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|
|
|
| [p] I41/amd |
a, b, pc |
x + (1/2), y, (1/p)z - (1/4); |
x, y + (1/2), (1/p)z; |
4a(b‡ ); ((p - 1)/2) × 8e |
4b(a‡ ); ((p - 1)/2) × 8e |
8c(d§ ); ((p - 1)/2) × 16h |
8d(c§ ); ((p - 1)/2) × 16h |
p × 8e |
|
|
+(0, 0, (u/p)) |
+(0, 0, (u/p)) |
|
16f; ((p - 1)/2) × 32i |
16g; ((p - 1)/2) × 32i |
p × 16h |
p × 32i |
|
p = prime = 4n - 1; u = 0, . . ., p - 1 |
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|
| [9] I41/amd |
3a, 3b, c |
(1/3)x, (1/3)y, z; |
(1/3)x, (1/3)y + (1/2), z; |
4a; 16g; 16h |
4b; 16g; 16h |
8c; 16f; 16h; 32i |
8d; 16f; 16h; 32i |
8e; 2 × 16h; 32i |
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±((1/3), 0, 0); ±(0, (1/3), 0); |
|
3 × 16f; 3 × 32i |
3 × 16g; 3 × 32i |
3 × 16h; 3 × 32i |
9 × 32i |
|
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±((1/3), (1/3), 0); ±((1/3), (2/3), 0) |
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|
| [p2] I41/amd |
pa, pb, c |
(1/p)x, (1/p)y, z; |
(1/p)x, (1/p)y + s, z; |
4a; ((p - 1)/2) × 16g; |
4b; ((p - 1)/2) × 16g; |
8c; ((p - 1)/2) × 16f; |
8d; ((p - 1)/2) × 16f; |
8e; |
|
|
+((u/p), (v/p), 0) |
+((u/p), (v/p), 0) |
((p - 1)/2) × 16h; |
((p - 1)/2) × 16h; |
((p - 1)/2) × 16h; |
((p - 1)/2) × 16h; |
(p - 1) × 16h; |
|
p = prime > 2; |
(((p - 1)(p - 3))/8) × 32i |
(((p - 1)(p - 3))/8) × 32i |
(((p - 1)2)/4) × 32i |
(((p - 1)2)/4) × 32i |
(((p - 1)2)/4) × 32i |
|
u, v = 1, . . ., p - 1 |
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s = 0 if p = 4n + 1; |
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p × 16f; |
p × 16g; |
p × 16h; |
p2 × 32i |
|
s = (1/2) if p = 4n - 1 |
|
((p(p - 1))/2) × 32i |
((p(p - 1))/2) × 32i |
((p(p - 1))/2) × 32i |
|
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| * origin 2 and p = 8n + 5 |
† origin 1 and p = 8n + 5 |
| ‡ origin 2 and p = 8n + 3 |
§ origin 1 and p = 8n + 3 |
