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Axes |
Coordinates |
Wyckoff positions |
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12a |
12b |
16c |
24d |
48e |
| I Maximal translationengleiche subgroups |
| [2] I213 (199) |
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12b |
12b |
2 × 8a |
2 × 12b |
2 × 24c |
| [4] R3c |
(1/2)(-a + b + c), |
y + z, x + z, x + y |
6b |
6b |
2a; 6b |
2 × 6b |
4 × 6b |
| (161) |
(1/2)(a - b + c), |
(rhombohedral |
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(1/2)(a + b - c) |
axes) |
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-a + b, -b + c, |
(1/3)(-2x + y + z), (1/3)(-x - y + 2z), |
18b |
18b |
6a; 18b |
2 × 18b |
4 × 18b |
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(1/2)(a + b + c) |
(2/3)(x + y + z) |
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(hexagonal axes) |
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| conjugate: |
a + b, -b - c, |
(1/3)(2x + y - z), (1/3)(x - y - 2z) + (1/2), |
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(1/2)(-a + b - c) |
(2/3)(-x + y - z) |
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(hexagonal axes) |
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| conjugate: |
-a - b, b - c, |
(1/3)(-2x - y - z) + (1/2), (1/3)(-x + y - 2z), |
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(1/2)(a - b - c) |
(2/3)(x - y - z) |
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(hexagonal axes) |
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| conjugate: |
a - b, b + c, |
(1/3)(2x - y + z) - (1/2), (1/3)(x + y + 2z) - (1/2), |
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(1/2)(-a - b + c) |
(2/3)(-x - y + z) |
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(hexagonal axes) |
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| [3] I-42d (122) |
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x, y + (1/4), z - (1/8) |
4a; 8d |
4b; 8d |
16e |
8c; 2 × 8d |
3 × 16e |
| conjugate: |
b, c, a |
y, z + (1/4), x - (1/8) |
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| conjugate: |
c, a, b |
z, x + (1/4), y - (1/8) |
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| II Maximal klassengleiche subgroups |
| Enlarged unit cell, isomorphic |
| [27] I-43d |
3a, 3b, 3c |
(1/3)x, (1/3)y, (1/3)z; ±((1/3), 0, 0); |
12a; 24d; 6 × 48e |
12b; 24d; 6 × 48e |
3 × 16c; 8 × 48e |
3 × 24d; |
27 × 48e |
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±(0, (1/3), 0); ±(0, 0, (1/3)); |
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12 × 48e |
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±(0, (1/3), (1/3)); ±((1/3), 0, (1/3)); |
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±((1/3), (1/3), 0); ±(0, (1/3), (2/3)); |
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±((1/3), 0, (2/3)); ±((1/3), (2/3), 0); |
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±((1/3), (1/3), (1/3)); ±((1/3), (1/3), (2/3)); |
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±((1/3), (2/3), (1/3)); ±((2/3), (1/3), (1/3)) |
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| [p3] I-43d |
pa, pb, pc |
(1/p)x, (1/p)y, (1/p)z; +((u/p), (v/p), (w/p)) |
12a(b*); |
12b(a*); |
p × 16c; |
p × 24d; |
p3 × 48e |
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p = prime > 2; u, v, w = 1, . . ., p - 1 |
((p - 1)/2) × 24d; |
((p - 1)/2) × 24d; |
((p(p2 - 1))/3) × 48e |
((p(p2 - 1))/2) × 48e |
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((p(p2 - 1))/4) × 48e |
((p(p2 - 1))/4) × 48e |
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| * p = 8n + 5 or p = 8n + 7 |
