P4232 No. 208 O2


Axes Coordinates Wyckoff positions
2a 4b 4c 6d 6e 6f 8g
12h 12i 12j 12k 12l 24m
I Maximal translationengleiche subgroups
[2] P23 1a; 1b 4e 4e 3c; 3d 6g 6h 2 × 4e
  (195) 6f; 6i 2 × 6g 2 × 6h 12j 12j 2 × 12j
[4] R32 x + (1/4), y + (1/4), z + (1/4) 2c 1b; 3e 1a; 3d 6f 3d; 3e 3d; 3e 2c; 6f
  (155) (rhombohedral axes) 2 × 6f 2 × 6f 2 × 6f 2 × 3e; 6f 2 × 3d; 6f 4 × 6f
a - b, b - c, (1/3)(2x - y - z), (1/3)(x + y - 2z), 6c 3b; 9e 3a; 9d 18f 9d; 9e 9d; 9e 6c; 18f
a + b + c (1/3)(x + y + z) + (1/4) 2 × 18f 2 × 18f 2 × 18f 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),
-a + b - c (1/3)(-x + y - z) + (1/4)
(hexagonal axes)
 conjugate: a + b, -b + c, (1/3)(2x + y + z), (1/3)(x - y + 2z),
a - b - c (1/3)(x - y - z) + (1/4)
(hexagonal axes)
 conjugate: -a + b, -b - c, (1/3)(-2x + y - z), (1/3)(-x - y - 2z),
-a - b + c (1/3)(-x - y + z) + (1/4)
(hexagonal axes)
[3] P4222 x + (1/2), y, z 2d 4o 4n 2a; 2b; 2c 2f; 4l 2e; 4m 8p
  (93) 4i; 4j; 4k 4h; 2 × 4l 4g; 2 × 4m 4o; 8p 4n; 8p 3 × 8p
 conjugate: b, c, a y + (1/2), z, x
 conjugate: c, a, b z + (1/2), x, y
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[2] F4132 2a, 2b, 2c (1/2)x, (1/2)y, (1/2)z; +((1/2), 0, 0) 8a; 8b 16c; 16d 32e 48f 48g 48g 2 × 32e
  (210) 2 × 48f 96h 96h 2 × 48g 96h 2 × 96h
[2] F4132 2a, 2b, 2c (1/2)x + (1/4), (1/2)y + (1/4), (1/2)z + (1/4); +((1/2), 0, 0) 8a; 8b 32e 16c; 16d 48f 48g 48g 2 × 32e
  (210) 2 × 48f 96h 96h 96h 2 × 48g 2 × 96h
[4] I4132 2a, 2b, 2c (1/2)x, (1/2)y, (1/2)z; +((1/2), 0, 0); 16e 8a; 24h 8b; 24g 2 × 24f 12c; 12d; 24f 24g; 24h 16e; 48i
  (214) +(0, (1/2), 0); +(0, 0, (1/2)) 2 × 48i 4 × 24f 2 × 48i 2 × 24h; 48i 2 × 24g; 48i 4 × 48i
[4] I4132 2a, 2b, 2c (1/2)x + (1/4), (1/2)y + (1/4), (1/2)z + (1/4); +((1/2), 0, 0); 16e 8b; 24g 8a; 24h 2 × 24f 24g; 24h 12c; 12d; 24f 16e; 48i
  (214) +(0, (1/2), 0); +(0, 0, (1/2)) 2 × 48i 2 × 48i 4 × 24f 2 × 24g; 48i 2 × 24h; 48i 4 × 48i


Axes Coordinates Wyckoff positions
2a 4b 4c 6d 6e
6f 8g 12h 12i
12j 12k 12l 24m
   Enlarged unit cell, isomorphic
[27] P4232 3a, 3b, 3c (1/3)x, (1/3)y, (1/3)z; ±((1/3), 0, 0); 2a; 2 × 8g; 4c; 8g; 2 × 12l; 4b; 8g; 2 × 12k; 6d; 12h; 12i; 6e; 12i; 12k;
±(0, (1/3), 0); ±(0, 0, (1/3)); 12h; 24m 3 × 24m 3 × 24m 12j; 5 × 24m 12l; 5 × 24m
±(0, (1/3), (1/3)); ±((1/3), 0, (1/3));
±((1/3), (1/3), 0); ±(0, (1/3), (2/3)); 6f; 12j; 12k; 3 × 8g; 8 × 24m 3 × 12h; 3 × 12i;
±((1/3), 0, (2/3)); ±((1/3), (2/3), 0); 12l; 5 × 24m 12 × 24m 12 × 24m
±((1/3), (1/3), (1/3)); ±((1/3), (1/3), (2/3)); 3 × 12j; 12 × 24m 3 × 12l; 12 × 24m 3 × 12k; 27 × 24m
±((1/3), (2/3), (1/3)); ±((2/3), (1/3), (1/3)) 12 × 24m
[p3] P4232 pa, pb, pc (1/p)x, (1/p)y, (1/p)z; 2a; 4b(c*); ((p - 1)/2) × 8g; 4c(b*); ((p - 1)/2) × 8g; 6d; ((p - 1)/2) × 12h; 6e; ((p - 1)/2) × 12i;
+((u/p), (v/p), (w/p)) (p - 1) × 8g; (p - 1) × 12k(l*); (p - 1) × 12l(k*); ((p - 1)/2) × 12i; ((p - 1)/2) × 12k;
p = prime > 2; ((p - 1)/2) × 12h; ((p3 - 4p + 3)/6) × 24m ((p3 - 4p + 3)/6) × 24m ((p - 1)/2) × 12j; ((p - 1)/2) × 12l;
u, v, w = 1, . . ., p - 1 ((p3 - 7p + 6)/12) × (((p - 1)2(p + 2))/4) × (((p - 1)2(p + 2))/4) ×
24m 24m 24m
6f; ((p - 1)/2) × 12j; p × 8g; p × 12h; p × 12i;
((p - 1)/2) × 12k; ((p(p2 - 1))/3) × 24m ((p(p2 - 1))/2) × 24m ((p(p2 - 1))/2) × 24m
((p - 1)/2) × 12l;
(((p - 1)2(p + 2))/4) × 24m
p × 12j; p × 12k(l*); p × 12l(k*); p3 × 24m
((p(p2 - 1))/2) × 24m ((p(p2 - 1))/2) × 24m ((p(p2 - 1))/2) × 24m
* p = 4n - 1









































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