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Axes |
Coordinates |
Wyckoff positions |
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origin 1 |
origin 2 |
4a |
4b |
8c |
8d |
8e |
16f |
| I Maximal translationengleiche subgroups |
| [2] I-4 (82) |
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x, y + (1/4), z + (1/8) |
2a; 2c |
2b; 2d |
8g |
8g |
4e; 4f |
2 × 8g |
| [2] I41 (80) |
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x, y + (1/4), z |
4a |
4a |
8b |
8b |
2 × 4a |
2 × 8b |
| [2] I112/b (15) |
x, y - (1/4), z - (1/8) |
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4e |
4e |
4a; 4d |
4b; 4c |
2 × 4e |
2 × 8f |
![[conventional setting]](/graphics/sg/Wconv.gif) A112/a |
b, -a - b, c |
-x + y - (1/4), -x, z - (1/8) |
-x + y, -x, z |
| II Maximal klassengleiche subgroups |
| Enlarged unit cell, isomorphic |
| [3] I41/a |
a, b, 3c |
x + (1/2), y, (1/3)z - (1/4); |
x + (1/2), y, (1/3)z; |
4a; 8e |
4b; 8e |
8d; 16f |
8c; 16f |
3 × 8e |
3 × 16f |
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±(0, 0, (1/3)) |
±(0, 0, (1/3)) |
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| [5] I41/a |
a, b, 5c |
x, y, (1/5)z; |
x, y, (1/5)z; |
4a(b*); 2 × 8e |
4b(a*); 2 × 8e |
8d(c*); |
8c(d*); |
5 × 8e |
5 × 16f |
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±(0, 0, (1/5)); ±(0, 0, (2/5)) |
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2 × 16f |
2 × 16f |
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| [p] I41/a |
a, b, pc |
x, y, (1/p)z; |
x, y, (1/p)z; |
4a(b† ); |
4b(a† ); |
8c(d† † ) |
8d(c† † ); |
p × 8e |
p × 16f |
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+(0, 0, (u/p)) |
+(0, 0, (u/p)) |
((p - 1)/2) × 8e |
((p - 1)/2) × 8e |
((p - 1)/2) × 16f |
((p - 1)/2) × 16f |
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p = prime = 4n + 1; u = 1, . . ., p - 1 |
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| [p] I41/a |
a, b, pc |
x + (1/2), y, (1/p) z - (1/4); |
x + (1/2), y, (1/p) z; |
4a(b‡ ); |
4b(a‡ ); |
8d(c‡ ‡ ); |
8c(d‡ ‡ ); |
p × 8e |
p × 16f |
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+(0, 0, (u/p)) |
+(0, 0, (u/p)) |
((p - 1)/2) × 8e |
((p - 1)/2) × 8e |
((p - 1)/2) × 16f |
((p - 1)/2) × 16f |
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p = prime = 4n - 1; u = 1, . . ., p - 1 |
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| [5] I41/a |
a + 2b, |
(1/5)(x + 2y), |
(1/5)(x + 2y) + (1/2), |
4a; 16f |
4b; 16f |
8d; 2 × 16f |
8c; 2 × 16f |
8e; 2 × 16f |
5 × 16f |
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-2a + b, c |
(1/5)(-2x + y), z; |
(1/5)(-2x + y), z; |
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±((1/5), (3/5), 0); ±((2/5), (1/5), 0) |
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| [5] I41/a |
a - 2b, |
(1/5)(x - 2y), |
(1/5)(x - 2y) + (1/2), |
4a; 16f |
4b; 16f |
8d; 2 × 16f |
8c; 2 × 16f |
8e; 2 × 16f |
5 × 16f |
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2a + b, c |
(1/5)(2x + y), z; |
(1/5)(2x + y), z; |
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±((1/5), (2/5), 0); ±((3/5), (1/5), 0) |
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| [p] I41/a |
qa - rb, |
(1/p)(qx - ry), |
(1/p)(qx - ry), |
4a; ((p - 1)/4) × 16f |
4b; ((p - 1)/4) × 16f |
8c; |
8d; |
8e; |
p × 16f |
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ra + qb, c |
(1/p)(rx + qy), z; |
(1/p)(rx + qy) + s, z; |
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((p - 1)/2) × 16f |
((p - 1)/2) × 16f |
((p - 1)/2) × 16f |
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+((uq/p), (ur/p), 0) |
+((uq/p), (ur/p), 0) |
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p = q2 + r2 = prime = 4n + 1; |
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q = 2n + 1 ≥ 1; r = ± 4n'≠ 0; u = 1, . . ., p - 1 |
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s = 0 if q = 4n + 1; s = (1/2) if q = 4n - 1 |
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| [p] I41/a |
qa - rb, |
(1/p)(qx - ry), |
(1/p)(qx - ry) + (1/2), |
4a; ((p - 1)/4) × 16f |
4b; ((p - 1)/4) × 16f |
8d; |
8c; |
8e; |
p × 16f |
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ra + qb, c |
(1/p)(rx + qy), z; |
(1/p)(rx + qy) + s, z; |
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((p - 1)/2) × 16f |
((p - 1)/2) × 16f |
((p - 1)/2) × 16f |
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+((uq/p), (ur/p), 0) |
+((uq/p), (ur/p), 0) |
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p = q2 + r2 = prime = 4n + 1; |
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q = 2n + 1 ≥ 1; r = ± 4n' + 2; u = 1, . . ., p - 1 |
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s = 0 if q = 4n + 1; s = (1/2) if q = 4n - 1 |
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| [9] I41/a |
3a, 3b, c |
(1/3)x, (1/3)y, z; |
(1/3)x, (1/3)y + (1/2), z; |
4a; 2 × 16f |
4b; 2 × 16f |
8c; 4 × 16f |
8d; 4 × 16f |
8e; 4 × 16f |
9 × 16f |
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±((1/3), 0, 0); ±(0, (1/3), 0); ±((1/3), (1/3), 0); ±((1/3), (2/3), 0) |
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| [p2] I41/a |
pa, pb, c |
(1/p)x, (1/p)y, z; |
(1/p)x, (1/p)y + s, z; |
4a; ((p2 - 1)/4) × 16f |
4b; ((p2 - 1)/4) × 16f |
8c; |
8d; |
8e; |
p2 × 16f |
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+((u/p), (v/p), 0) |
+((u/p), (v/p), 0) |
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((p2 - 1)/2) × 16f |
((p2 - 1)/2) × 16f |
((p2 - 1)/2) × 16f |
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p = prime = 4n - 1; u, v = 1, . . ., p - 1 |
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s = 0 if p = 4n + 1; s = (1/2) if p = 4n - 1 |
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| * origin 2 |
| † origin 2 and p = 8n + 5 |
† † origin 1 and p = 8n + 5 |
| ‡ origin 2 and p = 8n - 1 |
‡ ‡ origin 1 and p = 8n - 1 |
