|
Axes |
Coordinates |
Wyckoff positions |
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|
origin 1 |
origin 2 |
2a |
2b |
4c |
4d |
8e |
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8f |
8g |
16h |
| I Maximal translationengleiche subgroups |
| [2] P-4m2 |
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x + (1/4), y - (1/4), z + (1/4) |
1a; 1c |
1b; 1d |
2e; 2f |
2 × 2g |
8l |
| (115) |
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4h; 4i |
4j; 4k |
2 × 8l |
| [2] P-421c |
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x + (1/4), y - (1/4), z + (1/4) |
2a |
2b |
4c |
4d |
8e |
| (114) |
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8e |
8e |
2 × 8e |
| [2] P42mc |
|
x + (1/2), y, z |
x + (1/4), y + (1/4), z |
2c |
2c |
2 × 2c |
2a; 2b |
8f |
| (105) |
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8f |
4d; 4e |
2 × 8f |
| [2] P42212 |
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x + (1/4), y - (1/4), z + (1/4) |
2a |
2b |
4c |
4d |
8g |
| (94) |
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4e; 4f |
8g |
2 × 8g |
| [2] P42/n |
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x, y + (1/2), z |
2a |
2b |
4f |
4e |
4c; 4d |
| (86) |
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8g |
8g |
2 × 8g |
| [2] Pmmn |
|
x, y, z + (1/4) |
|
2a(b*) |
2a(b*) |
2 × 2a(b*) |
2 × 2b(a*) |
4c; 4d |
| (59) |
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8g |
4e; 4f |
2 × 8g |
| [2] Ccce |
a + b, |
(1/2)(x + y), |
(1/2)(x + y), |
4a(b*) |
4b(a*) |
8g |
8h |
8c; 8d |
| (68) |
-a + b, c |
(1/2)(-x + y), z |
(1/2)(-x + y), z |
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8e; 8f |
16i |
2 × 16i |
| II Maximal klassengleiche subgroups |
| Enlarged unit cell, isomorphic |
| [3] P42/nmc |
a, b, 3c |
x, y, (1/3)z; |
x, y, (1/3)z; |
2a(b*); 4c |
2b(a*); 4c |
3 × 4c |
3 × 4d |
8e; 16h |
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±(0, 0, (1/3)) |
±(0, 0, (1/3)) |
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8f; 16h |
3 × 8g |
3 × 16h |
| [p] P42/nmc |
a, b, pc |
x, y, (1/p)z; |
x, y, (1/p)z; |
2a(b† ); ((p - 1)/2) × 4c |
2b(a† ); ((p - 1)/2) × 4c |
p × 4c |
p × 4d |
8e; ((p - 1)/2) × 16h |
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+(0, 0, (u/p)) |
+(0, 0, (u/p)) |
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8f; ((p - 1)/2) × 16h |
p × 8g |
p × 16h |
|
p = prime > 2; u = 1, . . ., p - 1 |
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| [9] P42/nmc |
3a, 3b, c |
(1/3)x, (1/3)y, z; |
(1/3)x, (1/3)y, z; |
2a(b*); 8f; 8g |
2b(a*); 8f; 8g |
4c; 2 × 8g; 16h |
4d; 2 × 8g; 16h |
8e; 4 × 16h |
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±((1/3), 0, 0); ±(0, (1/3), 0); |
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3 × 8f; 3 × 16h |
3 × 8g; 3 × 16h |
9 × 16h |
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±((1/3), (1/3), 0); ±((1/3), (2/3), 0) |
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| [p2] P42/nmc |
pa, pb, c |
(1/p)x, (1/p)y, z; |
(1/p)x, (1/p)y, z; |
2a(b† ); ((p - 1)/2) × 8f; |
2b(a† ); ((p - 1)/2) × 8f; |
4c; (p - 1) × 8g; |
4d; (p - 1) × 8g; |
8e; ((p2 - 1)/2) × 16h |
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+((u/p), (v/p), 0) |
+((u/p), (v/p), 0) |
((p - 1)/2) × 8g; |
((p - 1)/2) × 8g; |
(((p - 1)2)/4) × 16h |
(((p - 1)2)/4) × 16h |
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p = prime > 2; u, v = 1, . . ., p - 1 |
(((p - 1)(p - 3))/8) × 16h |
(((p - 1)(p - 3))/8) × 16h |
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p × 8f; |
p × 8g; |
p2 × 16h |
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((p(p - 1))/2) × 16h |
((p(p - 1))/2) × 16h |
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| * origin 2 |
| † origin 2 and p = 4n - 1 |
