|
Axes |
Coordinates |
Wyckoff positions |
|
|
|
2a |
2b |
4c |
4d |
4e |
8f |
|
|
|
|
8g |
8h |
8i |
8j |
16k |
| I Maximal translationengleiche subgroups |
| [2] I4 |
|
|
2a |
2a |
4b |
4b |
2 × 2a |
2 × 4b |
| (79) |
|
|
|
8c |
8c |
8c |
8c |
2 × 8c |
| [2] I222 |
|
|
2a |
2c |
2b; 2d |
4j |
4i |
2 × 4j |
| (23) |
|
|
|
8k |
4e; 4g |
4f; 4h |
8k |
2 × 8k |
| [2] F222 |
a - b, |
(1/2)(x - y), |
4a |
4b |
8h |
4c; 4d |
8g |
2 × 8h |
| (22) |
a + b, c |
(1/2)(x + y), z |
|
8e; 8f |
16k |
16k |
8i; 8j |
2 × 16k |
| II Maximal klassengleiche subgroups |
| Loss of centring translations |
| [2] P42212 |
|
|
2a |
2b |
4d |
4d |
4c |
2 × 4d |
| (94) |
|
|
|
4e; 4f |
8g |
8g |
8g |
2 × 8g |
| [2] P4222 |
|
x + (1/2), y, z |
2d |
2c |
2a; 2b |
2e; 2f |
4i |
4g; 4h |
| (93) |
|
|
|
8p |
4j; 4k |
4l; 4m |
4n; 4o |
2 × 8p |
| [2] P4212 |
|
x + (1/2), y, z + (1/4) |
2c |
2c |
4d |
2a; 2b |
2 × 2c |
2 × 4d |
| (90) |
|
|
|
8g |
8g |
8g |
4e; 4f |
2 × 8g |
| [2] P422 |
|
|
1a; 1d |
1b; 1c |
2e; 2f |
4i |
2g; 2h |
2 × 4i |
| (89) |
|
|
|
4j; 4k |
4l; 4m |
4n; 4o |
8p |
2 × 8p |
| Enlarged unit cell, isomorphic |
| [3] I422 |
a, b, 3c |
x, y, (1/3)z; ±(0, 0, (1/3)) |
2a; 4e |
2b; 4e |
4c; 8f |
4d; 8f |
3 × 4e |
3 × 8f |
|
|
|
|
8g; 16k |
8h; 16k |
8i; 16k |
8j; 16k |
3 × 16k |
| [p] I422 |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
2a; ((p - 1)/2) × 4e |
2b; ((p - 1)/2) × 4e |
4c; ((p - 1)/2) × 8f |
4d; ((p - 1)/2) × 8f |
p × 4e |
p × 8f |
|
p = prime > 2; |
|
8g; ((p - 1)/2) × 16k |
8h; ((p - 1)/2) × 16k |
8i; ((p - 1)/2) × 16k |
8j; ((p - 1)/2) × 16k |
p × 16k |
|
u = 1, . . ., p - 1 |
|
|
|
|
|
|
| [9] I422 |
3a, 3b, c |
(1/3)x, (1/3)y, z; |
2a; 8g; 8h |
2b; 8g; 8i |
4c; 8h; 8i; 16k |
4d; 2 × 8j; 16k |
4e; 2 × 16k |
8f; 4 × 16k |
|
|
±((1/3), 0, 0); ±(0, (1/3), 0); |
|
3 × 8g; 3 × 16k |
3 × 8h; 3 × 16k |
3 × 8i; 3 × 16k |
3 × 8j; 3 × 16k |
9 × 16k |
|
|
±((1/3), (1/3), 0); ±((1/3), (2/3), 0) |
|
|
|
|
|
|
| [p2] I422 |
pa, pb, c |
(1/p)x, (1/p)y, z; |
2a; ((p - 1)/2) × 8g; |
2b; ((p - 1)/2) × 8g; |
4c; ((p - 1)/2) × 8h; |
4d; (p - 1) × 8j; |
4e; ((p2 - 1)/4) × 16k |
8f; ((p2 - 1)/2) × 16k |
|
|
+((u/p), (v/p), 0) |
((p - 1)/2) × 8h; |
((p - 1)/2) × 8i; |
((p - 1)/2) × 8i; |
(((p - 1)2)/4) × 16k |
|
|
|
p = prime > 2; |
(((p - 1)(p - 3))/8) × 16k |
(((p - 1)(p - 3))/8) × 16k |
(((p - 1)2)/4) × 16k |
|
|
|
|
u, v = 1, . . ., p - 1 |
|
p × 8g; |
p × 8h; |
p × 8i; |
p × 8j; |
p2 × 16k |
|
|
|
|
((p(p - 1))/2) × 16k |
((p(p - 1))/2) × 16k |
((p(p - 1))/2) × 16k |
((p(p - 1))/2) × 16k |
|
