|
Axes |
Coordinates |
Wyckoff positions |
|
|
|
2a |
2b |
4c |
4d |
4e |
6f |
|
|
|
6g |
8h |
12i |
12j |
12k |
24l |
| I Maximal translationengleiche subgroups |
| [2] P-62m |
|
x, y, z + (1/4) |
1a; 1b |
2e |
2c; 2d |
4h |
2 × 2e |
6i |
| (189) |
|
|
3f; 3g |
2 × 4h |
12l |
6j; 6k |
2 × 6i |
2 × 12l |
| [2] P-6c2 |
|
|
2b |
2a |
2d; 2f |
2c; 2e |
4g |
6j |
| (188) |
|
|
6k |
4h; 4i |
2 × 6j |
2 × 6k |
12l |
2 × 12l |
| [2] P63cm |
|
|
2a |
2a |
4b |
4b |
2 × 2a |
6c |
| (185) |
|
|
6c |
2 × 4b |
12d |
12d |
2 × 6c |
2 × 12d |
| [2] P6322 |
|
x, y, z + (1/4) |
2a |
2b |
4f |
2c; 2d |
4e |
6h |
| (182) |
|
|
6g |
2 × 4f |
2 × 6h |
12i |
12i |
2 × 12i |
| [2] P63/m |
|
|
2a |
2b |
2c; 2d |
4f |
4e |
6g |
| (176) |
|
|
6h |
2 × 4f |
12i |
2 × 6h |
12i |
2 × 12i |
| [2] P-3c1 |
|
|
2a |
2b |
4d |
4d |
4c |
6e |
| (165) |
|
|
6f |
2 × 4d |
12g |
12g |
12g |
2 × 12g |
| [2] P-31m |
|
|
2e |
1a; 1b |
4h |
2c; 2d |
2 × 2e |
3f; 3g |
| (162) |
|
|
6k |
2 × 4h |
6i; 6j |
12l |
2 × 6k |
2 × 12l |
| [3] Cmcm |
2a + b, b, c |
(1/2)x, -(1/2)x + y, z |
4c |
4a |
8g |
8e |
8f |
4b; 8d |
| (63) |
|
|
4c; 8g |
16h |
8e; 16h |
3 × 8g |
8f; 16h |
3 × 16h |
| conjugate: |
-a + b, -a - b, c |
(1/2)(-x + y), -(1/2)(x + y), z |
|
|
|
|
|
|
| conjugate: |
-a - 2b, a, c |
-(1/2)y, x - (1/2)y, z |
|
|
|
|
|
|
| II Maximal klassengleiche subgroups |
| Enlarged unit cell, non-isomorphic |
| [3] P63/mmc |
a - b, |
(1/3)(2x - y), (1/3)(x + y), z; |
2b; 2c; 2d |
2a; 4f |
12j |
12i |
4e; 2 × 4f |
6g; 12k |
| (194) |
a + 2b, c |
±((1/3), (2/3), 0) |
3 × 6h |
24l |
12i; 24l |
3 × 12j |
3 × 12k |
3 × 24l |
| Enlarged unit cell, isomorphic |
| [3] P63/mcm |
a, b, 3c |
x, y, (1/3)z; ±(0, 0, (1/3)) |
2a; 4e |
2b; 4e |
4c; 8h |
4d; 8h |
3 × 4e |
6f; 12k |
|
|
|
6g; 12k |
3 × 8h |
12i; 24l |
12j; 24l |
3 × 12k |
3 × 24l |
| [p] P63/mcm |
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) × 8h |
4d; ((p - 1)/2) × 8h |
p × 4e |
6f; ((p - 1)/2) × 12k |
|
p = prime > 2; u = 1, . . ., p - 1 |
6g; ((p - 1)/2) × 12k |
p × 8h |
12i; ((p - 1)/2) × 24l |
12j; ((p - 1)/2) × 24l |
p × 12k |
p × 24l |
| [4] P63/mcm |
2a, 2b, c |
(1/2)x, (1/2)y, z; +((1/2), 0, 0); |
2a; 6g |
2b; 6f |
4c; 12j |
4d; 12i |
4e; 12k |
12i; 12k |
|
|
+(0, (1/2), 0); +((1/2), (1/2), 0) |
2 × 6g; 12j |
8h; 24l |
2 × 12i; 24l |
4 × 12j |
2 × 12k; 24l |
4 × 24l |
| [p2] P63/mcm |
pa, pb, c |
(1/p)x, (1/p)y, z; +((u/p), (v/p), 0) |
2a; |
2b; ((p - 1)/2) × 12i |
4c; ((p2 - 1)/3) × 12j |
4d; |
4e; |
6f; ((p - 1)/2) × 12i; |
|
p = prime > 4; u, v = 1, . . ., p - 1 |
(p - 1) × 6g; |
((p - 1)/2) × 12k; |
|
(p - 1) × 12i; |
(p - 1) × 12k; |
((p - 1)/2) × 12k; |
|
|
|
(((p - 1)(p - 2))/6) × |
(((p - 1)(p - 5))/12) × |
|
(((p - 1)(p - 2))/6) × |
(((p - 1)(p - 2))/6) × |
(((p - 1)2)/4) × 24l |
|
|
|
12j |
24l |
|
24l |
24l |
|
|
|
|
p × 6g; |
8h; |
p × 12i; |
p2 × 12j |
p × 12k; |
p2 × 24l |
|
|
|
((p(p - 1))/2) × 12j |
((p2 - 1)/3) × 24l |
((p(p - 1))/2) × 24l |
|
((p(p - 1))/2) × 24l |
|
