P21212 No. 18 D23


Axes Coordinates Wyckoff positions
2a 2b 4c
I Maximal translationengleiche subgroups
[2] P2111 (4) x, y + (1/4), z 2a 2a 2 × 2a
[conventional setting]P1211 c, a, b z, x, y + (1/4)
[2] P1211 (4) x + (1/4), y, z 2a 2a 2 × 2a
[2] P112 (3) 1a; 1d 1b; 1c 2 × 2e
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[2] P212121 (19) a, b, 2c x + (1/4), y, (1/2)z; +(0, 0, (1/2)) 4a 4a 2 × 4a
[2] P212121 (19) a, b, 2c x + (1/4), y, (1/2)z + (1/4); +(0, 0, (1/2)) 4a 4a 2 × 4a
   Enlarged unit cell, isomorphic
[3] P21212 3a, b, c (1/3)x, y, z; ±((1/3), 0, 0) 2a; 4c 2b; 4c 3 × 4c
[p] P21212 pa, b, c (1/p)x, y, z; +((u/p), 0, 0) 2a; (1/2)(p - 1) × 4c 2b; (1/2)(p - 1) × 4c p × 4c
p = prime > 2; u = 1, . . ., p - 1
[3] P21212 a, 3b, c x, (1/3)y, z; ±(0, (1/3), 0) 2a; 4c 2b; 4c 3 × 4c
[p] P21212 pa, b, c x, (1/p)y, z; +(0, (u/p), 0) 2a; (1/2)(p - 1) × 4c 2b; (1/2)(p - 1) × 4c p × 4c
p = prime > 2; u = 1, . . ., p - 1
[2] P21212 a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 2 × 2a 2 × 2b 2 × 4c
[2] P21212 a, b, 2c x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 2 × 2a 2 × 2b 2 × 4c
[3] P21212 a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) 3 × 2a 3 × 2b 3 × 4c
[p] P21212 a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) p × 2a p × 2b p × 4c
p = prime; u = 1, . . ., p - 1


Nonconventional settings
        interchange letters and sequences in Hermann-Mauguin symbols, axes and coordinates:
P22121 abca xyzx
P21221 abca xyzx










































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