|
Axes |
Coordinates |
Wyckoff positions |
|
|
|
2a |
2b |
2c |
2d |
2e |
2f |
4g |
|
|
|
4h |
4i |
4j |
4k |
4l |
4m |
8n |
| I Maximal translationengleiche subgroups |
| [2] P-4 (81) |
|
|
2e |
2g |
2f |
2g |
1a; 1b |
1c; 1d |
4h |
|
|
|
4h |
4h |
4h |
2 × 2e |
2 × 2f |
2 × 2g |
2 × 4h |
| [2] P222 |
|
x, y, z + (1/4) |
1a; 1d |
1c; 1f |
1e; 1h |
1b; 1g |
2q |
2t |
2j; 2m |
| (16) |
|
|
2k; 2p |
2l; 2o |
2i; 2n |
2 × 2q |
2 × 2t |
2r; 2s |
2 × 4u |
| [2] Ccc2 |
a - b, |
(1/2)(x - y), (1/2)(x + y), z |
4a |
4c |
4b |
4c |
4a |
4b |
8d |
| (37) |
a + b, c |
|
8d |
8d |
8d |
2 × 4a |
2 × 4b |
2 × 4c |
2 × 8d |
| II Maximal klassengleiche subgroups |
| Enlarged unit cell, non-isomorphic |
| [2] P-4n2 |
a - b, |
(1/2)(x - y), (1/2)(x + y), z; |
4e |
4f |
2c; 2d |
4g |
2a; 2b |
4h |
8i |
| (118) |
a + b, c |
+((1/2), (1/2), 0) |
2 × 4f |
2 × 4g |
8i |
2 × 4e |
2 × 4h |
8i |
2 × 8i |
| [2] P-4n2 |
a - b, |
(1/2)(x - y) + (1/2), |
2c; 2d |
4g |
4e |
4f |
4h |
2a; 2b |
2 × 4g |
| (118) |
a + b, c |
(1/2)(x + y), z; +((1/2), (1/2), 0) |
8i |
8i |
2 × 4f |
2 × 4h |
2 × 4e |
8i |
2 × 8i |
| [2] P-4c2 |
a - b, |
(1/2)(x - y), (1/2)(x + y), z; |
2a; 2b |
4e |
4i |
4f |
2c; 2d |
4i |
2 × 4e |
| (116) |
a + b, c |
+((1/2), (1/2), 0) |
8j |
8j |
2 × 4f |
4g; 4h |
2 × 4i |
8j |
2 × 8j |
| [2] P-4c2 |
a - b, |
(1/2)(x - y) + (1/2), |
4i |
4f |
2a; 2b |
4e |
4i |
2c; 2d |
8j |
| (116) |
a + b, c |
(1/2)(x + y), z; +((1/2), (1/2), 0) |
2 × 4f |
2 × 4e |
8j |
2 × 4i |
4g; 4h |
8j |
2 × 8j |
| Enlarged unit cell, isomorphic |
| [3] P-42c |
a, b, 3c |
x, y, (1/3)z; ±(0, 0, (1/3)) |
2a; 4k |
2d; 4m |
2c; 4l |
2b; 4m |
2e; 4k |
2f; 4l |
4j; 8n |
|
|
|
4i; 8n |
4h; 8n |
4g; 8n |
3 × 4k |
3 × 4l |
3 × 4m |
3 × 8n |
| [p] P-42c |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
2a; ((p - 1)/2) × 4k |
2b(d*); |
2c; ((p - 1)/2) × 4l |
2d(b*); |
2e; |
2f; |
4g(j*); |
|
p = prime > 2; u = 1, . . ., p - 1 |
|
((p - 1)/2) × 4m |
|
((p - 1)/2) × 4m |
((p - 1)/2) × 4k |
((p - 1)/2) × 4l |
((p - 1)/2) × 8n |
|
|
|
4h(i*); |
4i(h*); |
4j(g*); |
p × 4k |
p × 4l |
p × 4m |
p × 8n |
|
|
|
((p - 1)/2) × 8n |
((p - 1)/2) × 8n |
((p - 1)/2) × 8n |
|
|
|
|
| [9] P-42c |
3a, 3b, c |
(1/3)x, (1/3)y, z; |
2a; 4g; 4j; 8n |
2b; 4g; 4h; 8n |
2c; 4h; 4i; 8n |
2d; 4i; 4j; 8n |
2e; 2 × 8n |
2f; 2 × 8n |
3 × 4g; 3 × 8n |
|
|
±((1/3), 0, 0); ±(0, (1/3), 0); |
3 × 4h; 3 × 8n |
3 × 4i; 3 × 8n |
3 × 4j; 3 × 8n |
4k; 4 × 8n |
4l; 4 × 8n |
4m; 4 × 8n |
9 × 8n |
|
|
±((1/3), (1/3), 0); ±((1/3), (2/3), 0) |
|
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|
|
|
|
| [p2] P-42c |
pa, pb, c |
(1/p)x, (1/p)y, z; +((u/p), (v/p), 0) |
2a; ((p - 1)/2) × 4g; |
2b; ((p - 1)/2) × 4g; |
2c; ((p - 1)/2) × 4h; |
2d; ((p - 1)/2) × 4i; |
2e; |
2f; |
p × 4g; |
|
p = prime > 2; |
((p - 1)/2) × 4j; |
((p - 1)/2) × 4h; |
((p - 1)/2) × 4i; |
((p - 1)/2) × 4j; |
((p2 - 1)/4) × 8n |
((p2 - 1)/4) × 8n |
((p(p - 1))/2) × 8n |
|
u, v = 1, . . ., p - 1 |
(((p - 1)2)/4) × 8n |
(((p - 1)2)/4) × 8n |
(((p - 1)2)/4) × 8n |
(((p - 1)2)/4) × 8n |
|
|
|
|
|
|
p × 4h; |
p × 4i; |
p × 4j; |
4k; ((p2 - 1)/2) × 8n |
4l; |
4m; |
p2 × 8n |
|
|
|
((p(p - 1))/2) × 8n |
((p(p - 1))/2) × 8n |
((p(p - 1))/2) × 8n |
|
((p2 - 1)/2) × 8n |
((p2 - 1)/2) × 8n |
|
|
| * p = 4n - 1 |
