Fd-3c No. 228 F41/d-32/c Oh8


Axes Coordinates Wyckoff positions
origin 1 origin 2 16a 32b 32c 48d 64e 96f
96g 192h
I Maximal translationengleiche subgroups
[2] F-43c x + (1/8), y + (1/8), z + (1/8) 8a; 8b 32e 32e 24c; 24d 2 × 32e 48f; 48g
  (219) 96h 2 × 96h
[2] F4132 x - (1/8), y - (1/8), z - (1/8) 8a; 8b 16c; 16d 32e 48f 2 × 32e 2 × 48f
  (210) 2 × 48g 2 × 96h
[2] Fd-3 x + (1/4), y + (1/4), z + (1/4) 8a; 8b 32e 16c; 16d 48f 2 × 32e 2 × 48f
  (203) 96g 2 × 96g
[4] R-3c (1/2)(b+c), (1/2)(a+c), - x + y + z + (1/8), -x + y + z, 4c 2a; 6e 2b; 6d 12f 4c; 12f 2 × 12f
  (167) (1/2)(a + b) x - y + z + (1/8), x - y + z, 2 × 6e; 12f 4 × 12f
(rhombohedral axes) x + y - z + (1/8) x + y - z
(1/2)(-a + b), (1/2)(-b + c), (2/3)(-2x + y + z), (2/3)(-2x + y + z), 12c 6a; 18e 6b; 18d 36f 12c; 36f 2 × 36f
a + b + c (2/3)(-x - y + 2z), (2/3)(-x - y + 2z), 2 × 18e; 36f 4 × 36f
(hexagonal axes) (1/3)(x + y + z) + (1/8) (1/3)(x + y + z)
 conjugate: (1/2)(a + b), (1/2)(-b - c), (2/3)(2x + y - z), (2/3)(2x + y - z) + (1/2),
-a + b - c (2/3)(x - y - 2z), (2/3)(x - y - 2z) + (1/2),
(hexagonal axes) (1/3)(-x + y - z) + (1/8) (1/3)(-x + y - z) + (1/2)
 conjugate: (1/2)(-a - b), (1/2)(b - c), (2/3)(-2x - y - z), (2/3)(-2x - y - z),
a - b - c (2/3)(-x + y - 2z), (2/3)(-x + y - 2z) + (1/2),
(hexagonal axes) (1/3)(x - y - z) + (1/8) (1/3)(x - y - z) + (1/2)
 conjugate: (1/2)(a - b), (1/2)(b + c), (2/3)(2x - y + z), (2/3)(2x - y + z) + (1/2),
-a - b + c (2/3)(x + y + 2z), (2/3)(x + y + 2z),
(hexagonal axes) (1/3)(-x - y + z) + (1/8) (1/3)(-x - y + z) + (1/2)
[3] I41/acd (1/2)(a - b), (1/2)(a + b), c x - y, x + y, z + (1/4) x - y, x + y, z 8b 16e 16c 8a; 16f 32g 16d; 2 × 16f
  (142) 16e; 32g 3 × 32g
 conjugate: (1/2)(b - c), (1/2)(b + c), a y - z, y + z, x + (1/4) y - z, y + z, x
 conjugate: (1/2)(-a + c), (1/2)(a + c), b -x + z, x + z, y + (1/4) -x + z, x + z, y
II Maximal klassengleiche subgroups
   Enlarged unit cell, isomorphic
[27] Fd-3c 3a, 3b, 3c (1/3)x + (1/4), (1/3)y + (1/4), (1/3)x, (1/3)y, (1/3)z; 16a; 32b; 64e; 32c; 64e; 48d; 96f; 3 × 64e; 3 × 96f;
(1/3)z + (1/4); 2 × 64e; 2 × 96g; 4 × 192h 6 × 192h 8 × 192h 12 × 192h
±((1/3), 0, 0); ±(0, (1/3), 0); ±(0, 0, (1/3)); 96f; 192h 3 × 192h
±(0, (1/3), (1/3)); ±((1/3), 0, (1/3)); ±((1/3), (1/3), 0); 3 × 96g; 27 × 192h
±(0, (1/3), (2/3)); ±((1/3), 0, (2/3)); ±((1/3), (2/3), 0); 12 × 192h
±((1/3), (1/3), (1/3)); ±((2/3), (1/3), (1/3)); ±((1/3), (2/3), (1/3));
±((1/3), (1/3), (2/3))


Axes Coordinates Wyckoff positions
origin 1 origin 2 16a 32b 32c 48d 64e
96f 96g 192h
[p3] Fd-3c a, pb, pc (1/p)x + s, (1/p)y + s, (1/p)x, (1/p)y, (1/p)z; 16a; (p - 1) × 64e; 32b; ((p - 1)/2) × 64e; 32c; ((p - 1)/2) × 64e; 48d; ((p - 1)/2) × 96f; p × 64e;
(1/p)z + s; +((u/p), (v/p), (w/p)) ((p - 1)/2) × 96f; (p - 1) × 96g; ((p(p2 - 1))/6) × 192h ((p(p2 - 1))/4) × 192h ((p(p2 - 1))/3) × 192h
+((u/p), (v/p), (w/p)) (((p - 1)(p - 2)(p + 3))/12) × ((p3 - 4p + 3)/6) × 192h
s = 0  if p = 4n + 1; 192h
s = (1/4) if p = 4n - 1 p × 96f; p × 96g; p3 × 192h
p = prime > 2; ((p(p2 - 1))/2) × 192h ((p(p2 - 1))/2) × 192h
u, v, w = 1, . . ., p - 1









































to end of page
to top of page