|
Axes |
Coordinates |
Wyckoff positions |
|
|
|
4a |
4b |
4c |
8d |
| I Maximal translationengleiche subgroups |
| [2] P43 (78) |
|
|
4a |
4a |
4a |
2 × 4a |
| [2] P2221 (17) |
|
x, y, z + (1/4) |
2a; 2c |
2b; 2d |
4e |
2 × 4e |
| [2] C2221 (20) |
a + b, -a + b, c |
(1/2)(x + y), (1/2)(-x + y), z - (1/8) |
8c |
8c |
4a; 4b |
2 × 8c |
| II Maximal klassengleiche subgroups |
| Enlarged unit cell, non-isomorphic |
| [2] P43212 (96) |
a + b, -a + b, c |
(1/2)(x + y), (1/2)(-x + y), z; +((1/2), (1/2), 0) |
2 × 4a |
8b |
8b |
2 × 8b |
| [2] P43212 (96) |
a + b, -a + b, c |
(1/2)(x + y) + (1/2), (1/2)(-x + y), z; +((1/2), (1/2), 0) |
8b |
2 × 4a |
8b |
2 × 8b |
| Enlarged unit cell, isomorphic |
| [3] P4122 (91) |
a, b, 3c |
x, y, (1/3)z; ±(0, 0, (1/3)) |
4a; 8d |
4b; 8d |
4c; 8d |
3 × 8d |
| [p] P4122 (91) |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
4a; ((p - 1)/2) × 8d |
4b; ((p - 1)/2) × 8d |
4c; ((p - 1)/2) × 8d |
p × 8d |
|
p = prime = 4n - 1; u = 1, . . ., p - 1 |
|
|
|
|
| [5] P4322 |
a, b, 5c |
x, y, (1/5)z; ±(0, 0, (1/5)); ±(0, 0, (2/5)) |
4a; 2 × 8d |
4b; 2 × 8d |
4c; 2 × 8d |
5 × 8d |
| [p] P4322 |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
4a; ((p - 1)/2) × 8d |
4b; ((p - 1)/2) × 8d |
4c; ((p - 1)/2) × 8d |
p × 8d |
|
p = prime = 4n + 1; u = 1, . . ., p - 1 |
|
|
|
|
| [2] P4322 |
a + b, -a + b, c |
(1/2)(x + y), (1/2)(-x + y), z + (1/8); +((1/2), (1/2), 0) |
2 × 4c |
8d |
4a; 4b |
2 × 8d |
| [2] P4322 |
a + b, -a + b, c |
(1/2)(x + y) + (1/2), (1/2)(-x + y), z + (1/8); +((1/2), (1/2), 0) |
8d |
2 × 4c |
4a; 4b |
2 × 8d |
| [9] P4322 |
3a, 3b, c |
(1/3)x, (1/3)y, z; ±((1/3), 0, 0); ±(0, (1/3), 0); |
3 × 4a; 3 × 8d |
3 × 4b; 3 × 8d |
3 × 4c; 3 × 8d |
9 × 8d |
|
|
±((1/3), (1/3), 0); ±((1/3), (2/3), 0) |
|
|
|
|
| [p2] P4322 |
pa, pb, c |
(1/p)x, (1/p)y, z; +((u/p), (v/p), 0) |
p × 4a; |
p × 4b; |
p × 4c; |
p2 × 8d |
|
p = prime > 2; u, v = 1, . . ., p - 1 |
((p(p - 1))/2) × 8d |
((p(p - 1))/2) × 8d |
((p(p - 1))/2) × 8d |
|
