C2221 No. 20 D25


Axes Coordinates Wyckoff positions
4a 4b 8c
I Maximal translationengleiche subgroups
[2] C211 (5) 2a; 2b 4c 2 × 4c
[conventional setting]C121 -b, a, c -y, x, z
[2] C121 (5) x, y, z + (1/4) 4c 2a; 2b 2 × 4c
[2] P1121 (4) (1/2)(a - b), (1/2)(a + b), c x - y, x + y, z 2a 2a 2 × 2a
II Maximal klassengleiche subgroups
   Loss of centring translations
[2] P212121 (19) x + (1/4), y, z 4a 4a 2 × 4a
[2] P22121 (18) x + (1/4), y, z 2a; 2b 4c 2 × 4c
[conventional setting]P21212 b, c, a y, z, x + (1/4)
[2] P21221 (18) x, y + (1/4), z + (1/4) 4c 2a; 2b 2 × 4c
[conventional setting]P21212 c, a, b z + (1/4), x, y + (1/4)
[2] P2221 (17) 2a; 2b 2c; 2d 2 × 4e
   Enlarged unit cell, isomorphic
[3] C2221 3a, b, c (1/3)x, y, z; ±((1/3), 0, 0) 3 × 4a 4b; 8c 3 × 8c
[p] C2221 pa, b, c (1/p)x, y, z; +((u/p), 0, 0) p × 4a 4b; (1/2)(p - 1) × 8c p × 8c
p = prime > 2; u = 1, . . ., p - 1
[3] C2221 a, 3b, c x, (1/3)y, z; ±(0, (1/3), 0) 4a; 8c 3 × 4b 3 × 8c
[p] C2221 a, pb, c x, (1/p)y, z; +(0, (u/p), 0) 4a; (1/2)(p - 1) × 8c p × 4b p × 8c
p = prime > 2; u = 1, . . ., p - 1
[3] C2221 a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) 4a; 8c 4b; 8c 3 × 8c
[p] C2221 a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) 4a; (1/2)(p - 1) × 8c 4b; (1/2)(p - 1) × 8c p × 8c
p = prime > 2; u = 1, . . ., p - 1


Nonconventional settings
        interchange letters and sequences in Hermann-Mauguin symbols, axes and coordinates:
A2122 CA abca xyzx
B2212 CB abca xyzx










































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