|
Axes |
Coordinates |
Wyckoff positions |
|
|
|
4a |
4b |
8c |
24d |
| I Maximal translationengleiche subgroups |
| [2] P213 (198) |
|
|
4a |
4a |
2 × 4a |
2 × 12b |
| [4] R-3 (148) |
(rhombohedral axes) |
|
1a; 3e |
1b; 3d |
2c; 6f |
4 × 6f |
|
a - b, b - c, a + b + c |
(1/3)(2x - y - z), (1/3)(x + y - 2z), |
3a; 9e |
3b; 9d |
6c; 18f |
4 × 18f |
|
(hexagonal axes) |
(1/3)(x + y + z) |
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| conjugate: |
-a - b, b + c, -a + b - c |
(1/3)(-2x - y + z), (1/3)(-x + y + 2z) - (1/2), |
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(hexagonal axes) |
(1/3)(-x + y - z) |
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| conjugate: |
a + b, -b + c, a - b - c |
(1/3)(2x + y + z) - (1/2), (1/3)(x - y + 2z), |
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(hexagonal axes) |
(1/3)(x - y - z) |
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| conjugate: |
-a + b, -b - c, -a - b + c |
(1/3)(-2x + y - z) + (1/2), (1/3)(-x - y - 2z) + (1/2), |
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(hexagonal axes) |
(1/3)(-x - y + z) |
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| [3] Pbca (61) |
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4a |
4b |
8c |
3 × 8c |
| II Maximal klassengleiche subgroups |
| Enlarged unit cell, isomorphic |
| [27]Pa-3 |
3a, 3b, 3c |
(1/3)x, (1/3)y, (1/3)z; ±((1/3), 0, 0); ±(0, (1/3), 0); |
4a; 8c; 4 × 24d |
4b; 8c; 4 × 24d |
3 × 8c; 8 × 24d |
27 × 24d |
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±(0, 0, (1/3)); ±(0, (1/3), (1/3)); ±((1/3), 0, (1/3)); |
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±((1/3), (1/3), 0); ±(0, (1/3), (2/3)); ±((1/3), 0, (2/3)); |
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±((1/3), (2/3), 0); ±((1/3), (1/3), (1/3)); ±((2/3), (1/3), (1/3)); |
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±((1/3), (2/3), (1/3)); ±((1/3), (1/3), (2/3)) |
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| [p3] Pa-3 |
pa, pb, pc |
(1/p)x, (1/p)y, (1/p)z; +((u/p), (v/p), (w/p)) |
4a; ((p - 1)/2) × 8c; |
4b; ((p - 1)/2) × 8c; |
p × 8c; |
p3 × 24d |
|
p = prime > 2; |
u, v, w = 1, . . ., p - 1 |
((p(p2 - 1))/6) × 24d |
((p(p2 - 1))/6) × 24d |
((p(p2 - 1))/3) × 24d |
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