|
Axes |
Coordinates |
Wyckoff positions |
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8a |
8b |
24c |
24d |
32e |
48f |
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48g |
96h |
| I Maximal translationengleiche subgroups |
| [2] F23 |
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4a; 4b |
4c; 4d |
24g |
24f |
2 × 16e |
2 × 24f |
| (196) |
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2 × 24g |
2 × 48h |
| [4] R3c |
(1/2)(b + c), (1/2)(a + c), |
-x + y + z, x - y + z, |
2a |
2a |
6b |
6b |
2a; 6b |
2 × 6b |
| (161) |
(1/2)(a + b) |
x + y - z |
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2 × 6b |
4 × 6b |
|
(rhombohedral axes) |
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(1/2)(-a + b), (1/2)(-b + c), |
(2/3)(-2x + y + z), |
6a |
6a |
18b |
18b |
6a; 18b |
2 × 18b |
|
a + b + c |
(2/3)(-x - y + 2z), |
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2 × 18b |
4 × 18b |
|
(hexagonal axes) |
(1/3)(x + y + z) |
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| conjugate: |
(1/2)(a + b), (1/2)(-b - c), |
(2/3)(2x + y - z), |
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-a + b - c |
(2/3)(x - y - 2z), |
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(hexagonal axes) |
(1/3)(-x + y - z) |
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| conjugate: |
(1/2)(-a - b), (1/2)(b - c), |
(2/3)(-2x - y - z), |
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a - b - c |
(2/3)(-x + y - 2z), |
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(hexagonal axes) |
(1/3)(x - y - z) |
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| conjugate: |
(1/2)(a - b), (1/2)(b + c), |
(2/3)(2x - y + z), |
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-a - b + c |
(2/3)(x + y + 2z), |
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(hexagonal axes) |
(1/3)(-x - y + z) |
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| [3] I-4c2 |
(1/2)(a - b), (1/2)(a + b), c |
x - y, x + y, z + (1/4) |
4a |
4d |
4c; 8h |
4b; 8e |
16i |
2 × 8e; 8f |
| (120) |
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8g; 2 × 8h |
3 × 16i |
| conjugate: |
(1/2)(b - c), (1/2)(b + c), a |
y - z, y + z, x + (1/4) |
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| conjugate: |
(1/2)(-a + c), (1/2)(a + c), b |
-x + z, x + z, y + (1/4) |
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| II Maximal klassengleiche subgroups |
| Loss of centring translations |
| [4] P-43n |
4 conjugate |
|
2a; 6b |
8e |
24i |
6c; 6d; 12f |
8e; 24i |
2 × 12f; 12g; 12h |
| (218) |
subgroups |
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2 × 24i |
4 × 24i |
| [4] P-43n |
4 conjugate |
x + (1/4), y + (1/4), z + (1/4) |
8e |
2a; 6b |
6c; 6d; 12f |
24i |
8e; 24i |
2 × 24i |
| (218) |
subgroups |
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2 × 12f; 12g; |
4 × 24i |
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12h |
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| Enlarged unit cell, isomorphic |
| [27] F-43c |
3a, 3b, 3c |
(1/3)x, (1/3)y, (1/3)z; ±((1/3), 0, 0); |
8a; 2 × 32e; |
8b; 2 × 32e; |
24c; 48g; |
24d; 48f; |
3 × 32e; |
3 × 48f; |
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±(0, (1/3), 0); ±(0, 0, (1/3)); |
48f; 96h |
48g; 96h |
6 × 96h |
6 × 96h |
8 × 96h |
12 × 96h |
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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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3 × 48g; |
27 × 96h |
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±((1/3), 0, (2/3)); ±((1/3), (2/3), 0); |
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12 × 96h |
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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] F-43c |
pa, pb, pc |
(1/p)x, (1/p)y, (1/p)z; +((u/p), (v/p), (w/p)) |
8a; |
8b; |
24c; |
24d; |
p × 32e; |
p × 48f; |
|
p = prime > 2; u, v, w = 1, . . ., p - 1 |
(p - 1) × 32e; |
(p - 1) × 32e; |
((p - 1)/2) × 48g; |
((p - 1)/2) × 48f; |
((p(p2 - 1))/3) × 96h |
((p(p2 - 1))/2) × 96h |
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((p - 1)/2) × 48f; |
((p - 1)/2) × 48g; |
((p(p2 - 1))/4) × |
((p(p2 - 1))/4) × |
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((p3 - 7p + 6)/12) × |
((p3 - 7p + 6)/12) × |
96h |
96h |
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96h |
96h |
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p × 48g; |
p3 × 96h |
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((p(p2 - 1))/2) × 96h |
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