C222 No. 21 D26


Axes Coordinates Wyckoff positions
2a 2b 2c 2d 4e 4f 4g 4h 4i 4j
4k 8l
I Maximal translationengleiche subgroups
[2] C211 (5) 2a 2a 2b 2b 2 × 2a 2 × 2b 4c 4c 4c 4c
[conventional setting]C121 -b, a, c -y, x, z 4c 2 × 4c
[2] C121 (5) 2a 2a 2b 2b 4c 4c 2 × 2a 2 × 2b 4c 4c
4c 2 × 4c
[2] P112 (3) (1/2)(a - b), x - y, x + y, z 1a 1d 1d 1a 2e 2e 2e 2e 2 × 1a 2 × 1d
(1/2)(a + b), c 1b; 1c 2 × 2e
II Maximal klassengleiche subgroups
   Loss of centring translations
[2] P21212 (18) 2a 2b 2b 2a 4c 4c 4c 4c 2 × 2a 2 × 2b
4c 2 × 4c
[2] P2122 (17) x, y + (1/4), z 2a 2a 2b 2b 4e 4e 2 × 2a 2 × 2b 4e 4e
[conventional setting]P2221 b, c, a y + (1/4), z, x 2c; 2d 2 × 4e
[2] P2212 (17) x + (1/4), y + (1/4), z 2c 2c 2d 2d 2 × 2c 2 × 2d 4e 4e 4e 4e
[conventional setting]P2221 c, a, b z, x + (1/4), y + (1/4) 2a; 2b 2 × 4e
[2] P222 (16) 1a; 1e 1b; 1c 1f; 1g 1d; 1h 2i; 2k 2j; 2l 2m; 2o 2n; 2p 2q; 2t 2r; 2s
4u 2 × 4u
   Enlarged unit cell, non-isomorphic
[2] I212121 (24) a, b, 2c x + (1/4), y, (1/2)z; 4b 4b 4a 4a 8d 2 × 4a 2 × 4b 8d 8d 8d
+(0, 0, (1/2)) 2 × 4c 2 × 8d
[2] I212121 (24) a, b, 2c x + (1/4), y, (1/2)z + (1/4); 4a 4a 4b 4b 2 × 4a 8d 8d 2 × 4b 8d 8d
+(0, 0, (1/2)) 2 × 4c 2 × 8d
[2] I222 (23) a, b, 2c x, y, (1/2)z; 2a; 2c 2b; 2d 4j 4i 4e; 4f 8k 4g; 4h 8k 2 × 4i 2 × 4j
+(0, 0, (1/2)) 8k 2 × 8k
[2] I222 (23) a, b, 2c x, y, (1/2)z + (1/4); 4i 4j 2b; 2d 2a; 2c 8k 4e; 4f 8k 4g; 4h 2 × 4i 2 × 4j
+(0, 0, (1/2)) 8k 2 × 8k
[2] C2221 (20) a, b, 2c x, y, (1/2)z; 4a 4a 4b 4b 2 × 4a 8c 8c 2 × 4b 8c 8c
+(0, 0, (1/2)) 8c 2 × 8c
[2] C2221 (20) a, b, 2c x, y, (1/2)z + (1/4); 4b 4b 4a 4a 8c 2 × 4a 2 × 4b 8c 8c 8c
+(0, 0, (1/2)) 8c 2 × 8c
   Enlarged unit cell, isomorphic
[3] C222 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; 8l 4h; 8l 4i; 8l 4j; 8l
4k; 8l 3 × 8l
[p] C222 pa, b, c (1/p)x, y, z; +((u/p), 0, 0) 2a; 2b; 2c; 2d; p × 4e p × 4f 4g; 4h; 4i; 4j;
p = prime > 2; ((p - 1)/2) × 4e ((p - 1)/2) × 4e ((p - 1)/2) × 4f ((p - 1)/2) × 4f ((p - 1)/2) × 8l ((p - 1)/2) × 8l ((p - 1)/2) × 8l ((p - 1)/2) × 8l
u = 1, . . ., p - 1 4k; p × 8l
((p - 1)/2) × 8l
[3] C222 a, 3b, c x, (1/3)y, z; ±(0, (1/3), 0) 2a; 4g 2b; 4g 2c; 4h 2d; 4h 4e; 8l 4f; 8l 3 × 4g 3 × 4h 4i; 8l 4j; 8l
4k; 8l 3 × 8l
[p] C222 a, pb, c x, (1/p)y, z; +(0, (u/p), 0) 2a; 2b; 2c; 2d; 4e; 4f; p × 4g p × 4h 4i; 4j;
p = prime > 2; ((p - 1)/2) × 4g ((p - 1)/2) × 4g ((p - 1)/2) × 4h ((p - 1)/2) × 4h ((p - 1)/2) × 8l ((p - 1)/2) × 8l ((p - 1)/2) × 8l ((p - 1)/2) × 8l
u = 1, . . ., p - 1 4k; p × 8l
((p - 1)/2) × 8l
[2] C222 a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 2a; 2d 2b; 2c 4j 4i 4e; 4f 8l 4g; 4h 8l 2 × 4i 2 × 4j
2 × 4k 2 × 8l
[2] C222 a, b, 2c x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 4i 4j 2b; 2c 2a; 2d 8l 4e; 4f 8l 4g; 4h 2 × 4i 2 × 4j
2 × 4k 2 × 8l
[3] C222 a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) 2a; 4i 2b; 4j 2c; 4j 2d; 4i 4e; 8l 4f; 8l 4g; 8l 4h; 8l 3 × 4i 3 × 4j
3 × 4k 3 × 8l
[p] C222 a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) 2a; 2b; 2c; 2d; 4e; 4f; 4g; 4h; p × 4i p × 4j
p × 4k p × 8l
p = prime > 2; ((p - 1)/2) × 4i ((p - 1)/2) × 4j ((p - 1)/2) × 4j ((p - 1)/2) × 4i ((p - 1)/2) × 8l ((p - 1)/2) × 8l ((p - 1)/2) × 8l ((p - 1)/2) × 8l
u = 1, . . ., p - 1


Nonconventional settings
        interchange letters and sequences in Hermann-Mauguin symbols, axes and coordinates:
A222 C → A a→ b → c → a x→ y → z → x
B222 C→ B a← b ← c ← a x← y ← z ← x









































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