|
Axes |
Coordinates |
Wyckoff positions |
|
|
origin 1 |
origin 2 |
4a |
4b |
4c |
4d |
4e |
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|
|
|
8f |
8g |
8h |
8i |
16j |
| I Maximal translationengleiche subgroups |
| [2] P-4c2 (116) |
|
|
x + (1/4), y - (1/4), |
2a; 2b |
2c; 2d |
4e |
4f |
4i |
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|
|
z + (1/4) |
4g; 4h |
2 × 4e |
2 × 4f |
8j |
2 × 8j |
| [2] P-421m(113) |
|
|
x + (1/4), y - (1/4), |
4d |
2a; 2b |
4e |
4e |
2 × 2c |
|
|
|
z + (1/4) |
2 × 4d |
8f |
8f |
2 × 4e |
2 × 8f |
| [2] P42cm (101) |
|
x + (1/2), y, z |
x + (1/4), |
4c |
4c |
4d |
4d |
2a; 2b |
|
|
|
y + (1/4), z |
2 × 4c |
8e |
8e |
2 × 4d |
2 × 8e |
| [2] P42212 (94) |
|
x, y, z - (1/4) |
x + (1/4), y - (1/4), z |
2a; 2b |
4c |
4e |
4f |
4d |
|
|
|
|
2 × 4c |
2 × 4e |
2 × 4f |
8g |
2 × 8g |
| [2] P42/n (86) |
|
|
x + (1/2), y, z |
4f |
2a; 2b |
4c |
4d |
4e |
|
|
|
|
2 × 4f |
8g |
8g |
8g |
2 × 8g |
| [2] Pccn (56) |
|
x + (1/4), y - (1/4), |
|
4d |
4d |
4b |
4a |
4c |
|
|
z - (1/4) |
|
2 × 4d |
8e |
8e |
8e |
2 × 8e |
| [2] Cmme (67) |
a - b, |
(1/2)(x - y) - (1/4), |
(1/2)(x - y), |
4a; 4b |
8l |
4d; 4e |
4c; 4f |
2 × 4g |
|
a + b, c |
(1/2)(x + y), z - (1/4) |
(1/2)(x + y), z |
2 × 8l |
8i; 8j |
8h; 8k |
8m; 8n |
2 × 16o |
| II Maximal klassengleiche subgroups |
| Enlarged unit cell, isomorphic |
| [3] P42/ncm |
a, b, 3c |
x, y, (1/3)z; |
x, y, (1/3)z; |
4a; 8f |
4b; 8f |
4c(d*); 8i |
4d(c*); 8i |
3 × 4e |
|
|
±(0, 0, (1/3)) |
±(0, 0, (1/3)) |
3 × 8f |
8g(h*); 16j |
8h(g*); 16j |
3 × 8i |
3 × 16j |
| [p] P42/ncm |
a, b, pc |
x, y, (1/p)z; |
x, y, (1/p)z; |
4a; ((p - 1)/2) × 8f |
4b; ((p - 1)/2) × 8f |
4c(d† ); ((p - 1)/2) × 8i |
4d(c† ); ((p - 1)/2) × 8i |
p × 4e |
|
|
+(0, 0, (u/p)) |
+(0, 0, (u/p)) |
p × 8f |
8g(h† ); ((p - 1)/2) × 16j |
8h(g† ); ((p - 1)/2) × 16j |
p × 8i |
p × 16j |
|
p = prime > 2; u = 1, . . ., p - 1 |
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|
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|
| [9] P42/ncm |
3a, 3b, c |
(1/3)x, (1/3)y, z; |
(1/3)x, (1/3)y, z; |
4a; 8g; 8h; 16j |
4b; 2 × 16j |
4c; 8g; 8i; 16j |
4d; 8h; 8i; 16j |
4e; 2 × 8i; 16j |
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±((1/3), 0, 0); ±(0, (1/3), 0); |
8f; 4 × 16j |
3 × 8g; 3 × 16j |
3 × 8h; 3 × 16j |
3 × 8i; 3 × 16j |
9 × 16j |
|
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±((1/3), (1/3), 0); ±((1/3), (2/3), 0) |
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|
| [p2] P42/ncm |
pa, pb, c |
(1/p)x, (1/p)y, z; |
(1/p)x, (1/p)y, z; |
4a; ((p - 1)/2) × 8g; |
4b; ((p2 - 1)/4) × 16j |
4c; ((p - 1)/2) × 8g; |
4d; ((p - 1)/2) × 8h; |
4e; (p - 1) × 8i; |
|
|
+((u/p), (v/p), 0) |
+((u/p), (v/p), 0) |
((p - 1)/2) × 8h; |
|
((p - 1)/2) × 8i; |
((p - 1)/2) × 8i; |
(((p - 1)2)/4) × 16j |
|
p = prime > 2; |
(((p - 1)2)/4) × 16j |
|
(((p - 1)2)/4) × 16j |
(((p - 1)2)/4) × 16j |
|
|
u, v = 1, . . ., p - 1 |
8f; ((p2 - 1)/2) × 16j |
p × 8g; |
p × 8h; |
p × 8i; |
p2 × 16j |
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((p(p - 1))/2) × 16j |
((p(p - 1))/2) × 16j |
((p(p - 1))/2) × 16j |
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| * origin 1 |
| † origin 1 and p = 4n - 1 |
