I23 No. 197 T3


Axes Coordinates Wyckoff positions
2a 6b 8c 12d 12e 24f
I Maximal translationengleiche subgroups
[4] R3 (146) (1/2)(-a + b + c), y + z, x + z, x + y 1a 3b 1a; 3b 2 × 3b 2 × 3b 4 × 3b
(1/2)(a - b + c), (rhombohedral
(1/2)(a + b - c) axes)
-a + b, -b + c, (1/3)(-2x + y + z), (1/3)(-x - y + 2z), 3a 9b 3a; 9b 2 × 9b 2 × 9b 4 × 9b
(1/2)(a + b + c) (2/3)(x + y + z)
(hexagonal axes)
 conjugate: a + b, -b - c, (1/3)(2x + y - z), (1/3)(x - y - 2z),
(1/2)(-a + b - c) (2/3)(-x + y - z)
(hexagonal axes)
 conjugate: -a - b, b - c, (1/3)(-2x - y - z), (1/3)(-x + y - 2z),
(1/2)(a - b - c) (2/3)(x - y - z)
(hexagonal axes)
 conjugate: a - b, b + c, (1/3)(2x - y + z), (1/3)(x + y + 2z),
(1/2)(-a - b + c) (2/3)(-x - y + z)
(hexagonal axes)
[3] I222 (23) 2a 2b; 2c; 2d 8k 4e; 4g; 4i 4f; 4h; 4j 3 × 8k
II Maximal klassengleiche subgroups
   Loss of centring translations
[2] P23 (195) 1a; 1b 3c; 3d 2 × 4e 6f; 6i 6g; 6h 2 × 12j
   Enlarged unit cell, isomorphic
[27] I23 3a, 3b, 3c (1/3)x, (1/3)y, (1/3)z; ±((1/3), 0, 0); 2a; 2 × 8c; 12d; 6b; 12d; 2 × 12e; 3 × 8c; 3 × 12d; 3 × 12e; 27 × 24f
±(0, (1/3), 0); ±(0, 0, (1/3)); 24f 5 × 24f 8 × 24f 12 × 24f 12 × 24f
±(0, (1/3), (1/3)); ±((1/3), 0, (1/3));
±((1/3), (1/3), 0); ±(0, (1/3), (2/3));
±((1/3), 0, (2/3)); ±((1/3), (2/3), 0); ±((1/3), (1/3), (1/3));
±((1/3), (1/3), (2/3)); ±((1/3), (2/3), (1/3)); ±((2/3), (1/3), (1/3))
[p3] I23 pa, pb, pc (1/p)x, (1/p)y, (1/p)z; +((u/p), (v/p), (w/p)) 2a; (p - 1) × 8c; 6b; ((p - 1)/2) × 12d; p × 8c; p × 12d; p × 12e; p3 × 24f
p = prime > 2; ((p - 1)/2) × 12d; (p - 1) × 12e; ((p(p2 - 1))/3) × ((p(p2 - 1))/2) × ((p(p2 - 1))/2) ×
u, v, w = 1, . . ., p - 1 (((p - 1)(p - 2)(p + 3))/12) × (((p - 1)2(p + 2))/4) × 24f 24f 24f
24f 24f










































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