|
Axes |
Coordinates |
Wyckoff positions |
|
|
|
3a |
3b |
6c |
| I Maximal translationengleiche subgroups |
| [2] P31 (144) |
|
|
3a |
3a |
2 × 3a |
| [3] C121 (5) |
a, a + 2b, c |
x - (1/2)y, (1/2)y, z + (1/3) |
2a; 4c |
2b; 4c |
3 × 4c |
| conjugate: |
b, -2a - b, c |
-(1/2)x + y, -(1/2)x, z |
|
|
|
| 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 |
| [3] P3121 (152) |
a - b, a + 2b, c |
(1/3)(2x - y), (1/3)(x + y), z; ±((2/3), (1/3), 0) |
3a; 6c |
3b; 6c |
3 × 6c |
| [3] P3121 (152) |
a - b, a + 2b, c |
(1/3)(2x - y) - (1/3), (1/3)(x + y), z; ±((2/3), (1/3), 0) |
3a; 6c |
3b; 6c |
3 × 6c |
| [3] P3121 (152) |
a - b, a + 2b, c |
(1/3)(2x - y) + (1/3), (1/3)(x + y), z; ±((2/3), (1/3), 0) |
3a; 6c |
3b; 6c |
3 × 6c |
| Enlarged unit cell, isomorphic |
| [2] P3212 (153) |
a, b, 2c |
x, y, (1/2)z; +(0, 0, (1/2)) |
3a; 3b |
6c |
2 × 6c |
| [2] P3212 (153) |
a, b, 2c |
x, y, (1/2)z + (1/4); +(0, 0, (1/2)) |
6c |
3a; 3b |
2 × 6c |
| [5] P3212 (153) |
a, b, 5c |
x, y, (1/5) z; ±(0, 0, (1/5)); ±(0, 0, (2/5)) |
3a; 2 × 6c |
3b; 2 × 6c |
5 × 6c |
| [p] P3212 (153) |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
3a; ((p - 1)/2) × 6c |
3b; ((p - 1)/2) × 6c |
p × 6c |
|
p = prime = 6n - 1; u = 1, . . ., p - 1 |
|
|
|
| [7] P3112 |
a, b, 7c |
x, y, (1/7) z; ±(0, 0, (1/7)); ±(0, 0, (2/7)); ±(0, 0, (3/7)) |
3a; 3 × 6c |
3b; 3 × 6c |
7 × 6c |
| [p] P3112 |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
3a; ((p - 1)/2) × 6c |
3b; ((p - 1)/2) × 6c |
p × 6c |
|
p = prime = 6n + 1; u = 1, . . ., p - 1 |
|
|
|
| [4] P3112 |
2a, 2b, c |
(1/2)x, (1/2)y, z; +((1/2), 0, 0); +(0, (1/2), 0); +((1/2), (1/2), 0) |
2 × 3a; 6c |
2 × 3b; 6c |
4 × 6c |
| [p2] P3112 |
pa, pb, c |
(1/p)x, (1/p)y, z; +((u/p), (v/p), 0) |
p × 3a; ((p(p - 1))/2) × 6c |
p × 3b; ((p(p - 1))/2) × 6c |
p2 × 6c |
|
p = prime ≠ 3; u, v = 1, . . ., p - 1 |
|
|
|
