|
Axes |
Coordinates |
Wyckoff positions |
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8a |
8b |
24c |
24d |
48e |
48f |
64g |
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96h |
96i |
192j |
| I Maximal translationengleiche subgroups |
| [2] F-43c |
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8b |
8a |
24d |
24c |
48f |
48g |
2 × 32e |
| (219) |
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96h |
96h |
2 × 96h |
| [2] F432 |
|
x + (1/4), y + (1/4), z + (1/4) |
4a; 4b |
8c |
24d |
24e |
48i |
2 × 24e |
2 × 32f |
| (209) |
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48g; 48h |
96j |
2 × 96j |
| [2] Fm-3 |
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8c |
4a; 4b |
24e |
24d |
2 × 24e |
48g |
2 × 32f |
| (202) |
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96i |
2 × 48h |
2 × 96i |
| [4] R-3c |
(1/2)(b + c), (1/2)(a + c), |
-x + y + z, |
2a |
2b |
6e |
6d |
12f |
12f |
4c; 12f |
| (167) |
(1/2)(a + b) |
x - y + z, |
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2 × 6e; 12f |
2 × 12f |
4 × 12f |
|
(rhombohedral axes) |
x + y - z |
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(1/2)(-a + b), (1/2)(-b + c), |
(2/3)(-2x + y + z), |
6a |
6b |
18e |
18d |
36f |
36f |
12c; 36f |
|
a + b + c |
(2/3)(-x - y + 2z), |
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2 × 6e; 12f |
2 × 12f |
4 × 12f |
|
(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] I4/mcm |
(1/2)(a - b), (1/2)(a + b), c |
x - y + (1/2), x + y, z |
4a |
4d |
4b; 8h |
4c; 8e |
8g; 2 × 8h |
8f; 16i |
32m |
| (140) |
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16j; 32m |
16k; 2 × 16l |
3 × 32m |
| conjugate: |
(1/2)(b - c), (1/2)(b + c), a |
y - z + (1/2)z, y + z, x |
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| conjugate: |
(1/2)(-a + c), (1/2)(a + c), b |
-x + z + (1/2), x + z, y |
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| II Maximal klassengleiche subgroups |
| Loss of centring translations |
| [4] Pm-3n (223) |
|
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8e |
2a; 6b |
6c; 6d; 12f |
24k |
2 × 12f; 12g; 12h |
48l |
16i; 48l |
| 4 conjugate subgroups |
|
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2 × 24j; 48l |
4 × 24k |
4 × 48l |
| [4] Pn-3n (222) |
|
origin 1: x + (1/4), y + (1/4), z + (1/4) |
2a; 6b |
8c |
24h |
12d; 12e |
48i |
2 × 12e; 24g |
16f; 48i |
| 4 conjugate subgroups |
origin 2: x, y, z |
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2 × 24h; 48i |
2 × 48i |
4 × 48i |
| Enlarged unit cell, isomorphic |
| [27] Fm-3c |
3a, 3b, 3c |
(1/3)x, (1/3)y, (1/3)z; ±((1/3), 0, 0); |
8a; 48f; |
8b; 48e; |
24c; 48e; |
24d; 48f; |
3 × 48e; 6 × 96i; |
3 × 48f; |
3 × 64g; |
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±(0, (1/3), 0); ±(0, 0, (1/3)); |
64g; |
64g; |
96h; 3 × 96i; |
2 × 96i; |
3 × 192j |
6 × 192j |
8 × 192j |
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±(0, (1/3), (1/3)); ±((1/3), 0, (1/3)); |
96h |
96i |
192j |
2 × 192j |
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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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3 × 96h; |
9 × 96i; |
27 × 192j |
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±((1/3), (1/3), (1/3)); ±((1/3), (1/3), (2/3)); |
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12 × 192j |
9 × 192j |
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±((1/3), (2/3), (1/3)); ±((2/3), (1/3), (1/3)) |
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