|
Axes |
Coordinates |
Wyckoff positions |
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origin 1 |
origin 2 |
8a |
8b |
16c |
16d |
32e |
48f |
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96g |
| I Maximal translationengleiche subgroups |
| [2] F23 |
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x + (1/8), y + (1/8), |
4a; 4c |
4b; 4d |
16e |
16e |
2 × 16e |
24f; 24g |
| (196) |
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z + (1/8) |
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2 × 48h |
| [4] R-3 |
(1/2)(b + c), |
- x + y + z - (1/8), |
-x + y + z, |
2c |
2c |
1a; 3d |
1b; 3e |
2c; 6f |
2 × 6f |
| (148) |
(1/2)(a + c), |
x - y + z - (1/8), |
x - y + z, |
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4 × 6f |
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(1/2)(a + b) |
x + y - z - (1/8) |
x + y - z |
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(rhombohedral axes) |
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(1/2)(-a + b), |
(2/3)(-2x + y + z), |
(2/3)(-2x + y + z), |
6c |
6c |
3a; 9d |
3b; 9e |
6c; 18f |
2 × 18f |
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(1/2)(-b + c), |
(2/3)(-x - y + 2z), |
(2/3)(-x - y + 2z), |
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4 × 18f |
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a + b + c |
(1/3)(x + y + z) - (1/8) |
(1/3)(x + y + z) |
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(hexagonal axes) |
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| conjugate: |
(1/2)(a + b), |
(2/3)(2x + y - z), |
(2/3)(2x + y - z) + (1/2), |
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(1/2)(-b - c), |
(2/3)(x - y - 2z), |
(2/3)(x - y - 2z) + (1/2), |
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-a + b - c |
(1/3)(-x + y - z) - (1/8) |
(1/3)(-x + y - z) + (1/2) |
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(hexagonal axes) |
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| conjugate: |
(1/2)(-a - b), |
(2/3)(-2x - y - z), |
(2/3)(-2x - y - z), |
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(1/2)(b - c), |
(2/3)(-x + y - 2z), |
(2/3)(-x + y - 2z) + (1/2), |
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a - b - c |
(1/3)(x - y - z) - (1/8) |
(1/3)(x - y - z) + (1/2) |
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(hexagonal axes) |
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| conjugate: |
(1/2)(a - b), |
(2/3)(2x - y + z), |
(2/3)(2x - y + z) + (1/2), |
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(1/2)(b + c), |
(2/3)(x + y + 2z), |
(2/3)(x + y + 2z), |
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-a - b + c |
(1/3)( - x - y + z) - (1/8) |
(1/3)(-x - y + z) + (1/2) |
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(hexagonal axes) |
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| [3] Fddd |
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8a |
8b |
16c |
16d |
32h |
16e; 16f; 16g |
| (70) |
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3 × 32h |
| II Maximal klassengleiche subgroups |
| Enlarged unit cell, isomorphic |
| [27] Fd-3 |
3a, 3b, 3c |
(1/3)x - (1/4), (1/3)y - (1/4), |
(1/3)x, (1/3)y, (1/3)z; |
8b; |
8a; |
16c; 32e; |
16d; 32e; |
3 × 32e; |
3 × 48f; |
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(1/3)z - (1/4); |
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2 × 32e; |
2 × 32e; |
4 × 96g |
4 × 96g |
8 × 96g |
12 × 96g |
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±((1/3), 0, 0); ±(0, (1/3), 0); ±(0, 0, (1/3)); |
48f; 96g |
48f; 96g |
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±(0, (1/3), (1/3)); ±((1/3), 0, (1/3)); ±((1/3), (1/3), 0); |
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27 × 96g |
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±(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)); |
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±((1/3), (1/3), (2/3)) |
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| [p3] Fd-3 |
pa, pb, pc |
(1/p)x + s, (1/p)y + s, |
(1/p)x, (1/p)y, (1/p)z; |
8a(b*); |
4b(a*); |
16c; |
16d; |
p × 32e; |
p × 48f; |
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(1/p)z + s; +((u/p), (v/p), (w/p)) |
+((u/p), (v/p), (w/p)) |
(p - 1) × 32e; |
(p - 1) × 32e; |
((p - 1)/2) × 32e; |
((p - 1)/2) × 32e; |
((p(p2 - 1))/3) × |
((p(p2 - 1))/2) × 96g |
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p = prime > 2; u, v, w = 1, . . ., p - 1; |
((p - 1)/2) × 48f; |
((p - 1)/2) × 48f; |
((p(p2 - 1))/6) × |
((p(p2 - 1))/6) × |
96g |
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s = 0 if p = 8n + 1; s = - (1/4) if p = 8n + 3; |
((p3 - 7p + 6)/12) × |
((p3 - 7p + 6)/12) × |
96g |
96g |
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s = (1/2) if p = 8n + 5; s = (1/4) if p = 8n + 7 |
96g |
96g |
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p3 × 96g |
| * p = 8n± 3 |
