I222 No. 23 D28


Axes Coordinates Wyckoff positions
2a 2b 2c 2d 4e 4f 4g 4h 4i
4j 8k
I Maximal translationengleiche subgroups
[2] I211 (5) 2a 2a 2b 2b 2 × 2a 2 × 2b 4c 4c 4c
[conventional setting]I121 c, a, b z, x, y 4c 2 × 4c
[conventional setting]C121 -b - c, a, b -y, x, -y + z
[2] I121 (5) 2a 2b 2b 2a 4c 4c 2 × 2a 2 × 2b 4c
[conventional setting]C121 -a-c, b, a -z, y, x - z 4c 2 × 4c
[2] I112 (5) 2a 2b 2a 2b 4c 4c 4c 4c 2 × 2a
[conventional setting]A112 a, -a + b, c x + y, y, z 2 × 2b 2 × 4c
II Maximal klassengleiche subgroups
   Loss of centring translations
[2] P22121(18) x + (1/4), y, z 2a 2a 2b 2b 2 × 2a 2 × 2b 4c 4c 4c
[conventional setting]P21212 b, c, a y, z, x + (1/4) 4c 2 × 4c
[2] P21221(18) x, y + (1/4), z 2a 2b 2b 2a 4c 4c 2 × 2a 2 × 2b 4c
[conventional setting]P21212 c, a, b z, x, y + (1/4) 4c 2 × 4c
[2] P21212(18) x, y, z + (1/4) 2a 2b 2a 2b 4c 4c 4c 4c 2 × 2a
2 × 2b 2 × 4c
[2] P222 (16) 1a; 1h 1b; 1g 1d; 1e 1c; 1f 2i; 2l 2j; 2k 2m; 2p 2n; 2o 2q; 2t
2r; 2s 2 × 4u
   Enlarged unit cell, isomorphic
[3] I222 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; 8k 4h; 8k 4i; 8k
4j; 8k 3 × 8k
[p] I222 pa, b, c (1/p)x, y, z; +((u/p), 0, 0) 2a; 2b; 2c; 2d; p × 4e p × 4f 4g; 4h; 4i;
p = prime > 2; ((p - 1)/2) × 4e ((p - 1)/2) × 4e ((p - 1)/2) × 4f ((p - 1)/2) × 4f ((p - 1)/2) × 8k ((p - 1)/2) × 8k ((p - 1)/2) × 8k
u = 1, . . ., p - 1 4j; p × 8k
((p - 1)/2) × 8k
[3] I222 a, 3b, c x, (1/3)y, z; ±(0, (1/3), 0) 2a; 4g 2b; 4h 2c; 4h 2d; 4g 4e; 8k 4f; 8k 3 × 4g 3 × 4h 4i; 8k
4j; 8k 3 × 8k
[p] I222 a, pb, c x, (1/p)y, z; +(0, (u/p), 0) 2a; 2b; 2c; 2d; 4e; 4f; p × 4g p × 4h 4i;
p = prime > 2; ((p - 1)/2) × 4g ((p - 1)/2) × 4h ((p - 1)/2) × 4h ((p - 1)/2) × 4g ((p - 1)/2) × 8k ((p - 1)/2) × 8k ((p - 1)/2) × 8k
u = 1, . . ., p - 1 4j; p × 8k
((p - 1)/2) × 8k
[3] I222 a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) 2a; 4i 2b; 4j 2c; 4i 2d; 4j 4e; 8k 4f; 8k 4g; 8k 4h; 8k 3 × 4i
3 × 4j 3 × 8k
[p] I222 a, b, pc x, y, (1/p)y; +(0, 0, (u/p)) 2a; 2b; 2c; 2d; 4e; 4f; 4g; 4h; p × 4i
p = prime > 2; ((p - 1)/2) × 4i ((p - 1)/2) × 4j ((p - 1)/2) × 4i ((p - 1)/2) × 4j ((p - 1)/2) × 8k ((p - 1)/2) × 8k ((p - 1)/2) × 8k ((p - 1)/2) × 8k
u = 1, . . ., p - 1 p × 4j p × 8k









































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