|
Axes |
Coordinates |
Wyckoff positions |
|
|
|
4a |
8b |
| I Maximal translationengleiche subgroups |
| [2] I112 (5) |
|
|
2a; 2b |
2 × 4c |
![[conventional setting]](/graphics/sg/Wconv.gif) A112 |
a, -a + b, c |
x + y, y, z |
| II Maximal klassengleiche subgroups |
| Loss of centring translations |
| [2] P43 (78) |
|
x + (1/4), y + (1/4), z |
4a |
2 × 4a |
| [2] P41 (76) |
|
x + (1/4), y - (1/4), z |
4a |
2 × 4a |
| Enlarged unit cell, isomorphic |
| [3] I41 |
b, -a, 3c |
y, -x, (1/3)z; ±(0, 0, (1/3)) |
3 × 4a |
3 × 8b |
| [p] I41 |
b, -a, pc |
y, -x, (1/p)z; +(0, 0, (u/p)) |
p × 4a |
p × 8b |
|
p = prime = 4n - 1; u = 1, . . ., p - 1 |
|
|
| [5] I41 |
a, b, 5c |
x, y, (1/5)z; ±(0, 0, (1/5)); ±(0, 0, (2/5)) |
5 × 4a |
5 × 8b |
| [p] I41 |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
p × 4a |
p × 8b |
|
p = prime = 4n + 1; u = 1, . . ., p - 1 |
|
|
| [5] I41 |
a + 2b, -2a + b, c |
(1/5)(x + 2y), (1/5)(-2x + y), z; ±((1/5), (3/5), 0); ±((2/5), (1/5), 0) |
4a; 2 × 8b |
5 × 8b |
| [5] I41 |
a - 2b, 2a + b, c |
(1/5)(x - 2y), (1/5)(2x + y), z; ±((1/5), (2/5), 0); ±((3/5), (1/5), 0) |
4a; 2 × 8b |
5 × 8b |
| [p] I41 |
qa - rb, |
(1/p)(qx - ry), (1/p)(rx + qy), z; +((uq/p), (ur/p), 0) |
4a; ((p - 1)/2) × 8b |
p × 8b |
|
ra + qb, c |
q = 2n + 1 ≥ 1; r = ± 2n'≠ 0; |
|
|
|
p = q2 + r2 = prime =4n+1; u = 1, . . ., p - 1 |
|
|
| [9] I41 |
3a, 3b, c |
(1/3)x, (1/3)y, z; ±((1/3), 0, 0); ±(0, (1/3), 0); |
4a; 4 × 8b |
9 × 8b |
|
|
±((1/3), (1/3), 0); ±((1/3), (2/3), 0) |
|
|
| [p2] I41 |
pa, pb, c |
(1/p)x, (1/p)y, z; +((u/p), (v/p), 0) |
4a; ((p2 - 1)/2) × 8b |
p2 × 8b |
|
p = prime = 4n - 1; u, v = 1, . . ., p - 1 |
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