|
Axes |
Coordinates |
Wyckoff positions |
|
|
|
4a |
12b |
| I Maximal translationengleiche subgroups |
| [4] R3 (146) |
(rhombohedral axes) |
1a; 3b |
4 × 3b |
|
a - b, b - c, a + b + c |
(1/3)(2x- y - z), (1/3)(x + y - 2z), |
3a; 9b |
4 × 9b |
|
(hexagonal axes) |
(1/3)(x + y + z) |
|
|
| conjugate: |
-a - b, b + c, -a + b - c |
(1/3)(-2x - y + z), (1/3)(-x + y + 2z) - (1/2), |
|
|
|
(hexagonal axes) |
(1/3)(-x + y - z) |
|
|
| conjugate: |
a + b, -b + c, a - b - c |
(1/3)(2x + y + z) - (1/2), (1/3)(x - y + 2z), |
|
|
|
(hexagonal axes) |
(1/3)(x - y - z) |
|
|
| conjugate: |
-a + b, -b - c, -a - b + c |
(1/3)(-2x + y - z) + (1/2), (1/3)(-x - y - 2z) + (1/2), |
|
|
|
(hexagonal axes) |
(1/3)(-x - y + z) |
|
|
| [3] P212121 (19) |
|
|
4a |
3 × 4a |
| II Maximal klassengleiche subgroups |
| Enlarged unit cell, isomorphic |
| [27] P213 |
3a, 3b, 3c |
(1/3)x, (1/3)y, (1/3)z; ±((1/3), 0, 0); ±(0, (1/3), 0); |
3 × 4a; 8 × 12b |
27 × 12b |
|
|
±(0, 0, (1/3)); ±((1/3), 0, (1/3)); ±((1/3), (1/3), 0); |
|
|
|
|
±(0, (1/3), (1/3)); ±(0, (1/3), (2/3)); ±((1/3), 0, (2/3)); ±((1/3), (2/3), 0); |
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|
|
±((1/3), (1/3), (1/3)); ±((2/3), (1/3), (1/3)); ±((1/3), (2/3), (1/3)); ±((1/3), (1/3), (2/3)) |
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|
| [p3] P213 |
pa, pb, pc |
(1/p)x, (1/p)y, (1/p)z; +((u/p), (v/p), (w/p)) |
p × 4a; ((p(p2 - 1))/3) × 12b |
p3 × 12b |
|
p = prime > 2; |
u, v, w = 1, . . ., p - 1 |
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