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Axes |
Coordinates |
Wyckoff positions |
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origin 1 |
origin 2 |
2a |
6b |
8c |
12d |
12e |
16f |
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24g |
24h |
48i |
| I Maximal translationengleiche subgroups |
| [2] P-43n |
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x + (1/4), y + (1/4), z + (1/4) |
2a |
6b |
8e |
6c; 6d |
12f |
2 × 8e |
| (218) |
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12g; 12h |
24i |
2 × 24i |
| [2] P432 |
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x + (1/4), y + (1/4), z + (1/4) |
1a; 1b |
3c; 3d |
8g |
12h |
6e; 6f |
2 × 8g |
| (207) |
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2 × 12h |
12i; 12j |
2 × 24k |
| [2] Pn-3 |
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2a |
6d |
4b; 4c |
12g |
12f |
2 × 8e |
| (201) |
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2 × 12g |
24h |
2 × 24h |
| [4] R-3c |
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x - (1/4), y - (1/4), z - (1/4) |
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2a |
6e |
2b; 6d |
12f |
12f |
4c; 12f |
| (167) |
(rhombohedral axes) |
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2 × 12f |
2 × 6e; 12f |
4 × 12f |
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a - b, b - c, |
(1/3)(2x - y - z), |
(1/3)(2x - y - z), |
6a |
18e |
6b; 18d |
36f |
36f |
12c; 36f |
|
a + b + c |
(1/3)(x + y - 2z), |
(1/3)(x + y - 2z), |
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2 × 36f |
2 × 18e; 36f |
4 × 36f |
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(hexagonal axes) |
(1/3)(x + y + z) - (1/4) |
(1/3)(x + y + z) |
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| conjugate: |
-a - b, b + c, |
(1/3)(-2x - y + z), |
(1/3)(-2x - y + z) + (1/2), |
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-a + b - c |
(1/3)(-x + y + 2z), |
(1/3)(-x + y + 2z) + (1/2), |
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(hexagonal axes) |
(1/3)(-x + y - z) - (1/4) |
(1/3)(-x + y - z) |
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| conjugate: |
a + b, -b + c, |
(1/3)(2x + y + z), |
(1/3)(2x + y + z), |
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a - b - c |
(1/3)(x - y + 2z), |
(1/3)(x - y + 2z) + (1/2), |
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(hexagonal axes) |
(1/3)(x - y - z) - (1/4) |
(1/3)(x - y - z) |
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| conjugate: |
-a + b, -b - c, |
(1/3)(-2x + y - z), |
(1/3)(-2x + y - z) + (1/2), |
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-a - b + c |
(1/3)(-x - y - 2z), |
(1/3)(-x - y - 2z), |
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(hexagonal axes) |
(1/3)(-x - y + z) - (1/4) |
(1/3)(-x - y + z) |
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| [3] P4/nnc |
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2a |
2b; 4c |
8f |
4d; 8j |
4e; 8i |
16k |
| (126) |
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8g; 2 × 8j |
8h; 16k |
3 × 16k |
| conjugate: |
b, c, a |
y, z, x |
y, z, x |
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| conjugate: |
c, a, b |
z, x, y |
z, x, y |
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| II Maximal klassengleiche subgroups |
| Enlarged unit cell, isomorphic |
| [27] Pn-3n |
3a, 3b, 3c |
(1/3)x, (1/3)y, (1/3)z; |
(1/3)x, (1/3)y, (1/3)z; |
2a; 12e; 16f; |
6b; 12e; 24g; |
8c; 16f; |
12d; 24g; |
3 × 12e; |
3 × 16f; |
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±((1/3), 0, 0); ±(0, (1/3), 0); ±(0, 0, (1/3)); |
24h |
24h; 2 × 48i |
4 × 48i |
6 × 48i |
6 × 48i |
8 × 48i |
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±(0, (1/3), (1/3)); ±((1/3), 0, (1/3)); ±((1/3), (1/3), 0); |
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3 × 24g; |
3 × 24h; |
27 × 48i |
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±(0, (1/3), (2/3)); ±((1/3), 0, (2/3)); ±((1/3), (2/3), 0); |
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12 × 48i |
12 × 48i |
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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] Pn-3n |
pa, pb, pc |
(1/p)x, (1/p)y, (1/p)z; |
(1/p)x, (1/p)y, (1/p)z; |
2a; ((p - 1)/2) × 12e; |
6b; ((p - 1)/2) × 12e; |
8c; |
12d; |
p × 12e; |
p × 16f; |
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+((u/p), (v/p), (w/p)) |
+((u/p), (v/p), (w/p)) |
((p - 1)/2) × 16f |
((p - 1)/2) × 24g; |
((p - 1)/2) × 16f; |
((p - 1)/2) × 24g; |
((p(p2 - 1))/4) × 48i |
((p(p2 - 1))/3) × |
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p = prime > 2; u, v, w = 1, . . ., p - 1 |
((p - 1)/2) × 24h; |
((p - 1)/2) × 24h; |
((p(p2 - 1))/6) × 48i |
((p(p2 - 1))/4) × 48i |
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48i |
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((p3 - 13p + 12)/24) × |
((p3 - 5p + 4)/8) × 48i |
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48i |
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p × 24g; |
p × 24h; |
p3 × 48i |
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((p(p2 - 1))/2) × 48i |
((p(p2 - 1))/2) × 48i |
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