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Axes |
Coordinates |
Wyckoff positions |
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2a |
2b |
2c |
2d |
4e |
4f |
4g |
4h |
4i |
4j |
8k |
8l |
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8m |
8n |
16o |
I Maximal translationengleiche subgroups |
[2] I2mm (44) |
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2a |
2a |
2b |
2b |
2 × 2a |
2 × 2b |
4c |
4c |
4d |
4d |
8e |
8e |
Imm2 |
b, c, a |
y, z, x |
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2 × 4d |
2 × 4c |
2 × 8e |
[2] Im2m (44) |
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2a |
2b |
2b |
2a |
4d |
4d |
2 × 2a |
2 × 2b |
4c |
4c |
8e |
2 × 4c |
Imm2 |
c, a, b |
z, x, y |
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8e |
2 × 4d |
2 × 8e |
[2] Imm2 (44) |
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2a |
2b |
2a |
2b |
4c |
4c |
4d |
4d |
2 × 2a |
2 × 2b |
8e |
2 × 4d |
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2 × 4c |
8e |
2 × 8e |
[2] I222 (23) |
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2a |
2b |
2c |
2d |
4e |
4f |
4g |
4h |
4i |
4j |
8k |
8k |
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8k |
8k |
2 × 8k |
[2] I2/m11 (12) |
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2a |
2b |
2c |
2d |
4g |
4h |
4i |
4i |
4i |
4i |
4e; 4f |
2 × 4i |
I12/m1 |
c, a, b |
z, x, y |
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8j |
8j |
2 × 8j |
C12/m1 |
-b - c, a, c |
-y, x, -y + z |
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[2] I12/m1 (12) |
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2a |
2c |
2d |
2b |
4i |
4i |
4g |
4h |
4i |
4i |
4e; 4f |
8j |
C12/m1 |
-a - c, b, a |
-z, y, x - z |
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2 × 4i |
8j |
2 × 8j |
[2] I112/m (12) |
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2a |
2d |
2b |
2c |
4i |
4i |
4i |
4i |
4g |
4h |
4e; 4f |
8j |
A112/m |
b, -a - b, c |
-x + y, -x, z |
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8j |
2 × 4i |
2 × 8j |
II Maximal klassengleiche subgroups |
Loss of centring translations |
[2] Pmmn (59) |
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origin 1: x, y, z + (1/4) |
2a |
2b |
2a |
2b |
4f |
4f |
4e |
4e |
2 × 2a |
2 × 2b |
4c; 4d |
2 × 4e |
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origin 2: x + (1/4), y + (1/4), z + (1/4) |
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2 × 4f |
8g |
2 × 8g |
[2] Pmnm (59) |
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origin 1: x, y + (1/4), z |
2a |
2b |
2b |
2a |
4e |
4e |
2 × 2a |
2 × 2b |
4f |
4f |
4c; 4d |
2 × 4f |
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origin 2: x + (1/4), y + (1/4), z + (1/4) |
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8g |
2 × 4e |
2 × 8g |
Pmmn |
c, a, b |
z, x, y + (1/4)(origin 1) |
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z + (1/4), x + (1/4), y + (1/4) |
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(origin 2) |
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[2] Pnmm (59) |
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origin 1: x + (1/4), y, z |
2a |
2a |
2b |
2b |
2 × 2a |
2 × 2b |
4f |
4f |
4e |
4e |
4c; 4d |
8g |
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origin 2: x + (1/4), y + (1/4), z + (1/4) |
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2 × 4e |
2 × 4f |
2 × 8g |
Pmmn |
b, c, a |
y, z, x + (1/4)(origin 1) |
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y + (1/4), z + (1/4), x + (1/4) |
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(origin 2) |
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[2] Pnnm (58) |
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2a |
2d |
2b |
2c |
4g |
4g |
4g |
4g |
4e |
4f |
8h |
8h |
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8h |
2 × 4g |
2 × 8h |
[2] Pnmn (58) |
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2a |
2c |
2d |
2b |
4g |
4g |
4e |
4f |
4g |
4g |
8h |
8h |
Pnnm |
c, a, b |
z, x, y |
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2 × 4g |
8h |
2 × 8h |
[2] Pmnn (58) |
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2a |
2b |
2c |
2d |
4e |
4f |
4g |
4g |
4g |
4g |
8h |
2 × 4g |
Pnnm |
b, c, a |
y, z, x |
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8h |
8h |
2 × 8h |
[2] Pnnn (48) |
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origin 1: x, y, z |
2a |
2b |
2c |
2d |
4g |
4h |
4i |
4j |
4k |
4l |
4e; 4f |
8m |
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origin 2: x + (1/4), y + (1/4), z + (1/4) |
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8m |
8m |
2 × 8m |
[2] Pmmm (47) |
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1a; 1h |
1b; 1g |
1c; 1f |
1d; 1e |
2i; 2l |
2j; 2k |
2m; 2p |
2n; 2o |
2q; 2t |
2r; 2s |
8 |
4u; 4v |
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4w; 4x |
4y; 4z |
2 × 8 |
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Axes |
Coordinates |
Wyckoff positions |
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2a |
2b |
2c |
2d |
4e |
4f |
4g |
4h |
4i |
4j |
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8k |
8l |
8m |
8n |
16o |
Enlarged unit cell, isomorphic |
[3] Immm |
3a, b, c |
(1/3)x, y, z; ±((1/3), 0, 0) |
2a; 4e |
2b; 4e |
2c; 4f |
2d; 4f |
3 × 4e |
3 × 4f |
4g; 8n |
4h; 8n |
4i; 8m |
4j; 8m |
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8k; 16o |
8l; 16o |
3 × 8m |
3 × 8n |
3 × 16o |
[p] Immm |
pa, b, c |
(1/p)x, y, z; +((u/p), 0, 0) |
2a; |
2b; |
2c; |
2d; |
p × 4e |
p × 4f |
4g; |
4h; |
4i; |
4j; |
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p = prime > 2; |
((p - 1)/2) × 4e |
((p - 1)/2) × 4e |
((p - 1)/2) × 4f |
((p - 1)/2) × 4f |
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((p - 1)/2) × 8n |
((p - 1)/2) × 8n |
((p - 1)/2) × 8m |
((p - 1)/2) × 8m |
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u = 1, . . ., p - 1 |
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8k; |
8l; |
p × 8m |
p × 8n |
p × 16o |
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((p - 1)/2) × 16o |
((p - 1)/2) × 16o |
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[3] Immm |
a, 3b, c |
x, (1/3)y, z; ±(0, (1/3), 0) |
2a; 4g |
2b; 4h |
2c; 4h |
2d; 4g |
4e; 8n |
4f; 8n |
3 × 4g |
3 × 4h |
4i; 8l |
4j; 8l |
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8k; 16o |
3 × 8l |
8m; 16o |
3 × 8n |
3 × 16o |
[p] Immm |
a, pb, c |
x, (1/p)y, z; +(0, (u/p), 0) |
2a; |
2b; |
2c; |
2d; |
4e; |
4f; |
p × 4g |
p × 4h |
4i; |
4j; |
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p = prime > 2; |
((p - 1)/2) × 4g |
((p - 1)/2) × 4h |
((p - 1)/2) × 4h |
((p - 1)/2) × 4g |
((p - 1)/2) × 8n |
((p - 1)/2) × 8n |
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((p - 1)/2) × 8l |
((p - 1)/2) × 8l |
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u = 1, . . ., p - 1 |
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8k; |
p × 8l |
8m; |
p × 8n |
p × 16o |
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((p - 1)/2) × 16o |
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((p - 1)/2) × 16o |
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[3] Immm |
a, b, 3c |
x, y, (1/3)z; ±(0, 0, (1/3)) |
2a; 4i |
2b; 4j |
2c; 4i |
2d; 4j |
4e; 8m |
4f; 8m |
4g; 8l |
4h; 8l |
3 × 4i |
3 × 4j |
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8k; 16o |
3 × 8l |
3 × 8m |
8n; 16o |
3 × 16o |
[p] Immm |
a, b, pc |
x, y, (1/p)z; +(0, 0, (u/p)) |
2a; |
2b; |
2c; |
2d; |
4e; |
4f; |
4g; |
4h; |
p × 4i |
p × 4j |
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p = prime > 2; |
((p - 1)/2) × 4i |
((p - 1)/2) × 4j |
((p - 1)/2) × 4i |
((p - 1)/2) × 4j |
((p - 1)/2) × 8m |
((p - 1)/2) × 8m |
((p - 1)/2) × 8l |
((p - 1)/2) × 8l |
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u = 1, . . ., p - 1 |
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8k; |
p × 8l |
p × 8m |
8n; |
p × 16o |
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((p - 1)/2) × 16o |
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((p - 1)/2) × 16o |
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