I4132 No. 214 O8




Axes Coordinates Wyckoff positions
8a 8b 12c 12d 16e 24f
24g 24h 48i
I Maximal translationengleiche subgroups
[2] I213 8a 8a 12b 12b 2 × 8a 2 × 12b
  (199) 24c 24c 2 × 24c
[4] R32 (1/2)(-a + b + c), y + z - (1/4), x + z - (1/4), x + y - (1/4) 1a; 3d 1b; 3e 3d; 3e 3d; 3e 2c; 6f 2 × 6f
  (155) (1/2)(a - b + c), (rhombohedral 2 × 3e; 6f 2 × 3d; 6f 4 × 6f
(1/2)(a + b - c) axes)
-a + b, -b + c, (1/3)(-2x + y + z), (1/3)(-x - y + 2z), 3a; 9d 3b; 9e 9d; 9e 9d; 9e 6c; 18f 2 × 18f
(1/2)(a + b + c) (2/3)(x + y + z) - (1/4) 2 × 9e; 18f 2 × 9d; 18f 4 × 18f
(hexagonal axes)
 conjugate: a + b, -b - c, (1/3)(2x + y - z), (1/3)(x - y - 2z) + (1/2),
(1/2)(-a + b - c) (2/3)(-x + y - z) - (1/4)
(hexagonal axes)
 conjugate: -a - b, b - c, (1/3)(-2x - y - z) + (1/2), (1/3)(-x + y - 2z),
(1/2)(a - b - c) (2/3)(x - y - z) - (1/4)
(hexagonal axes)
 conjugate: a - b, b + c, (1/3)(2x - y + z) + (1/2), (1/3)(x + y + 2z) + (1/2),
(1/2)(-a - b + c) (2/3)(-x - y + z) - (1/4)
(hexagonal axes)
[3] I4122 (98) x, y - (1/4), z - (1/8) 8e 8d 4a; 8f 4b; 8f 16g 8c; 2 × 8f
 conjugate: b, c, a y, z - (1/4), x - (1/8) 8d; 16g 8e; 16g 3 × 16g
 conjugate: c, a, b z, x - (1/4), y - (1/8)
II Maximal klassengleiche subgroups
   Loss of centring translations
[2] P4132 8c 4a; 4b 12d 12d 2 × 8c 24e
  (213) 2 × 12d 24e 2 × 24e
[2] P4332 4a; 4b 8c 12d 12d 2 × 8c 24e
  (212) 24e 2 × 12d 2 × 24e
   Enlarged unit cell, isomorphic
[27] I4132 3a, 3b, 3c (1/3)x, (1/3)y, (1/3)z; ±((1/3), 0, 0); 8b; 16e; 8a; 16e; 12c; 24f; 12d; 24f; 3 × 16e; 3 × 24f;
±(0, (1/3), 0); ±(0, 0, (1/3)); 2 × 24g; 2 × 24h; 24g; 24h; 24g; 24h; 8 × 48i 12 × 48i
±(0, (1/3), (1/3)); ±((1/3), 0, (1/3)); 3 × 48i 3 × 48i 5 × 48i 5 × 48i
±((1/3), (1/3), 0); ±((1/3), (1/3), (1/3));
±(0, (1/3), (2/3)); ±((1/3), 0, (2/3)); 3 × 24h; 3 × 24g; 27 × 48i
±((1/3), (2/3), 0); ±((1/3), (1/3), (2/3)); 12 × 48i 12 × 48i
±((1/3), (2/3), (1/3)); ±((2/3), (1/3), (1/3))
[p3] I4132 pa, pb, pc (1/p)x, (1/p)y, (1/p)z; +((u/p), (v/p), (w/p)) 8a(b*); 8b(a*); 12c(d† ); 12d(c† ); p × 16e; p × 24f;
p = prime > 2; u, v, w = 1, . . ., p - 1 ((p - 1)/2) × 16e; ((p - 1)/2) × 16e; ((p - 1)/2) × 24f; ((p - 1)/2) × 24f; ((p(p2 - 1))/3) × 48i ((p(p2 - 1))/2) × 48i
(p - 1) × (p - 1) × ((p - 1)/2) × 24g; ((p - 1)/2) × 24g;
24h(g*); 24g(h*); ((p - 1)/2) × 24h; ((p - 1)/2) × 24h;
((p3 - 4p + 3)/6) × ((p3 - 4p + 3)/6) × (((p - 1)2(p + 2))/4) × (((p - 1)2(p + 2))/4) ×
48i 48i 48i 48i
p × 24g(h*); p × 24h(g*); p3 × 48i
((p(p2 - 1))/2) × 48i ((p(p2 - 1))/2) × 48i
* p = 4n - 1 p = 8n' - 3   or p = 8n' - 1



















































































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