|
Axes |
Coordinates |
Wyckoff positions |
|
|
|
3a |
3b |
3c |
3d |
6e |
6f |
|
|
|
|
6g |
6h |
6i |
6j |
12k |
| I Maximal translationengleiche subgroups |
| [2] P62 (171) |
|
|
3a |
3a |
3b |
3b |
2 × 3a |
2 × 3b |
|
|
|
|
6c |
6c |
6c |
6c |
2 × 6c |
| [2] P3221 |
|
x, y, z - (1/3) |
3a |
3b |
3a |
3b |
6c |
6c |
| (154) |
|
|
|
2 × 3a |
2 × 3b |
6c |
6c |
2 × 6c |
| [2] P3212 |
|
x, y, z + (1/3) |
3a |
3b |
3a |
3b |
6c |
6c |
| (153) |
|
|
|
6c |
6c |
2 × 3a |
2 × 3b |
2 × 6c |
| [3] C222 |
a, a + 2b, c |
x - (1/2)y, (1/2)y, z |
2a; 4i |
2d; 4i |
2b; 4k |
2c; 4k |
3 × 4i |
4j; 2 × 4k |
| (21) |
|
|
|
4e; 8l |
4f; 8l |
4g; 8l |
4h; 8l |
3 × 8l |
| conjugate: |
b, -2a - b, c |
-(1/2)x + y, -(1/2)x, z + (1/3) |
|
|
|
|
|
|
| conjugate: |
-a - b, a - b, c |
-(1/2)(x + y), (1/2)(x - y), z - (1/3) |
|
|
|
|
|
|
| II Maximal klassengleiche subgroups |
| Enlarged unit cell, non-isomorphic |
| [2] P6122 |
a, b, 2c |
x, y, (1/2)z; +(0, 0, (1/2)) |
6a |
6b |
6a |
6b |
12c |
12c |
| (178) |
|
|
|
2 × 6a |
12c |
12c |
2 × 6b |
2 × 12c |
| [2] P6122 |
a, b, 2c |
x, y, (1/2)z + (1/4); +(0, 0, (1/2)) |
6b |
6a |
6b |
6a |
12c |
12c |
| (178) |
|
|
|
12c |
2 × 6a |
2 × 6b |
12c |
2 × 12c |
| Enlarged unit cell, isomorphic |
| [2] P6422 |
a, b, 2c |
x, y, (1/2)z; +(0, 0, (1/2)) |
3a; 3b |
6e |
3c; 3d |
6f |
2 × 6e |
2 × 6f |
| (181) |
|
|
|
6g; 6h |
12k |
6i; 6j |
12k |
2 × 12k |
| [2] P6422 |
a, b, 2c |
x, y, (1/2)z + (1/4); +(0, 0, (1/2)) |
6e |
3a; 3b |
6f |
3c; 3d |
2 × 6e |
2 × 6f |
| (181) |
|
|
|
12k |
6g; 6h |
12k |
6i; 6j |
2 × 12k |
| [5] P6422 |
a, b, 5c |
x, y, (1/5)z; ±(0, 0, (1/5)); |
3a; 2 × 6e |
3b; 2 × 6e |
3c; 2 × 6f |
3d; 2 × 6f |
5 × 6e |
5 × 6f |
| (181) |
|
±(0, 0, (2/5)) |
|
6g; 2 × 12k |
6h; 2 × 12k |
6i; 2 × 12k |
6j; 2 × 12k |
5 × 12k |
| [p] P6422 |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
3a; ((p - 1)/2) × 6e |
3b; ((p - 1)/2) × 6e |
3c; ((p - 1)/2) × 6f |
3d; ((p - 1)/2) × 6f |
p × 6e |
p × 6f |
| (181) |
p = prime = 6n - 1; u = 1, . . ., p - 1 |
|
6g; ((p - 1)/2) × 12k |
6h; ((p - 1)/2) × 12k |
6i; ((p - 1)/2) × 12k |
6j; ((p - 1)/2) × 12k |
p × 12k |
| [7] P6222 |
a, b, 7c |
x, y, (1/7) z; ±(0, 0, (1/7)) |
3a; 3 × 6e |
3b; 3 × 6e |
3c; 3 × 6f |
3d; 3 × 6f |
7 × 6e |
7 × 6f |
|
|
±(0, 0, (2/7)); ±(0, 0, (3/7)) |
|
6g; 3 × 12k |
6h; 3 × 12k |
6i; 3 × 12k |
6j; 3 × 12k |
7 × 12k |
| [p] P6222 |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
3a; ((p - 1)/2) × 6e |
3b; ((p - 1)/2) × 6e |
3c; ((p - 1)/2) × 6f |
3d; ((p - 1)/2) × 6f |
p × 6e |
p × 6f |
|
p = prime = 6n + 1; u = 1, . . ., p - 1 |
|
6g; ((p - 1)/2) × 12k |
6h; ((p - 1)/2) × 12k |
6i; ((p - 1)/2) × 12k |
6j; ((p - 1)/2) × 12k |
p × 12k |
| [3] P6222 |
2a + b, |
(1/3)(x + y), (1/3)(-x + 2y), |
3a; 6i |
3b; 6j |
3c; 6i |
3d; 6j |
6e; 12k |
6f; 12k |
|
-a + b, c |
z + (1/3); ±((1/3), (2/3), 0) |
|
3 × 6i |
3 × 6j |
6g; 12k |
6h; 12k |
3 × 12k |
| [4] P6222 |
2a, 2b, c |
(1/2)x, (1/2)y, z; +((1/2), 0, 0); |
3a; 3c; 6f |
3b; 3d; 6f |
6g; 6i |
6h; 6j |
6e; 3 × 6f |
2 × 12k |
|
|
+(0, (1/2), 0); +((1/2), (1/2), 0) |
|
2 × 6g; 12k |
2 × 6h; 12k |
2 × 6i; 12k |
2 × 6j; 12k |
4 × 12k |
| [p2] P6222 |
pa, pb, c |
(1/p)x, (1/p)y, z; +((u/p), (v/p), 0) |
3a; ((p - 1)/2) × 6g; |
3b; ((p - 1)/2) × 6h; |
3c; ((p - 1)/2) × 6g; |
3d; ((p - 1)/2) × 6h; |
6e; ((p2 - 1)/2) × 12k |
6f; ((p2 - 1)/2) × 12k |
|
p = prime > 4; |
((p - 1)/2) × 6i; |
((p - 1)/2) × 6j; |
((p - 1)/2) × 6i; |
((p - 1)/2) × 6j; |
|
|
|
u, v = 1, . . ., p - 1 |
(((p - 1)2)/4) × 12k |
(((p - 1)2)/4) × 12k |
(((p - 1)2)/4) × 12k |
(((p - 1)2)/4) × 12k |
|
|
|
|
|
|
p × 6g; |
p × 6h; |
p × 6i; |
p × 6j; |
p2 × 12k |
|
|
|
|
((p(p - 1))/2) × 12k |
((p(p - 1))/2) × 12k |
((p(p - 1))/2) × 12k |
((p(p - 1))/2) × 12k |
|
