P23 No. 195 T1


Axes Coordinates Wyckoff positions
1a 1b 3c 3d 4e 6f 6g
6h 6i 12j
I Maximal translationengleiche subgroups
[4] R3 (rhombohedral axes) 1a 1a 3b 3b 1a; 3b 2 × 3b 2 × 3b
  (146) 2 × 3b 2 × 3b 4 × 3b
a - b, b - c, (1/3)(2x - y - z), (1/3)(x + y - 2z), 3a 3a 9b 9b 3a; 9b 2 × 9b 2 × 9b
a + b + c (1/3)(x + y + z) 2 × 9b 2 × 9b 4 × 9b
(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)
(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)
(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)
(hexagonal axes)
[3] P222 1a 1h 1e; 1f; 1g 1b; 1c; 1d 4u 2i; 2m; 2q 2j; 2o; 2s
  (16) 2k; 2n; 2r 2l; 2p; 2t 3 × 4u
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[2] F23 2a, 2b, 2c (1/2)x, (1/2)y, (1/2)z; +((1/2), 0, 0) 4a; 4b 4c; 4d 24g 24f 2 × 16e 2 × 24f 48h
  (196) 48h 2 × 24g 2 × 48h
[4] I213 2a, 2b, 2c (1/2)x, (1/2)y, (1/2)z; +((1/2), 0, 0); 8a 8a 2 × 12b 2 × 12b 8a; 24c 2 × 24c 4 × 12b
  (199) +(0, (1/2), 0); +(0, 0, (1/2)) 2 × 24c 2 × 24c 4 × 24c
[4] I213 2a, 2b, 2c (1/2)x + (1/4), (1/2)y + (1/4), (1/2)z + (1/4); +((1/2), 0, 0); 8a 8a 2 × 12b 2 × 12b 8a; 24c 2 × 24c 2 × 24c
  (199) +(0, (1/2), 0); +(0, 0, (1/2)) 4 × 12b 2 × 24c 4 × 24c
[4] I23 2a, 2b, 2c (1/2)x, (1/2)y, (1/2)z; +((1/2), 0, 0); 2a; 6b 8c 24f 12d; 12e 8c; 24f 2 × 12d; 2 × 12e 2 × 24f
  (197) +(0, (1/2), 0); +(0, 0, (1/2)) 2 × 24f 2 × 24f 4 × 24f
[4] I23 2a, 2b, 2c (1/2)x + (1/4), (1/2)y + (1/4), (1/2)z + (1/4); +((1/2), 0, 0); 8c 2a; 6b 12d; 12e 24f 8c; 24f 2 × 24f 2 × 24f
  (197) +(0, (1/2), 0); +(0, 0, (1/2)) 2 × 24f 2 × 12d; 2 × 12e 4 × 24f


Axes Coordinates Wyckoff positions
1a 1b 3c 3d 4e 6f
6g 6h 6i 12j
   Enlarged unit cell, isomorphic
[27] P23 3a, 3b, 3c (1/3)x, (1/3)y, (1/3)z; ±((1/3), 0, 0); 1a; 2 × 4e; 6f; 1b; 2 × 4e; 6i; 3c; 6g; 6h; 3d; 6f; 6g; 3 × 4e; 3 × 6f;
±(0, (1/3), 0); ±(0, 0, (1/3)); 12j 12j 6i; 5 × 12j 6h; 5 × 12j 8 × 12j 12 × 12j
±(0, (1/3), (1/3)); ±((1/3), 0, (1/3));
±((1/3), (1/3), 0); ±(0, (1/3), (2/3)); 3 × 6g; 3 × 6h; 3 × 12i; 27 × 12j
±((1/3), 0, (2/3)); ±((1/3), (2/3), 0); 12 × 12j 12 × 12j 12 × 12j
±((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] P23 pa, pb, pc (1/p)x, (1/p)y, (1/p)z; 1a; (p - 1) × 4e; 1b; (p - 1) × 4e; 3c; ((p - 1)/2) × 6g; 3d; ((p - 1)/2) × 6f; p × 4e; p × 6f;
+((u/p), (v/p), (w/p)) ((p - 1)/2) × 6f; ((p - 1)/2) × 6i; ((p - 1)/2) × 6h; ((p - 1)/2) × 6g; ((p(p2 - 1))/3) × 12j ((p(p2 - 1))/2) × 12j
p = prime > 2; (((p - 1)(p - 2)(p + 3))/12) (((p - 1)(p - 2)(p + 3))/12) ((p - 1)/2) × 6i; ((p - 1)/2) × 6h;
u, v, w = 1, . . ., p - 1 × 12j × 12j (((p - 1)2(p + 2))/4) × (((p - 1)2(p + 2))/4) ×
12j 12j
p × 6g; p × 6h; p × 6i; p3 × 12j
((p(p2 - 1))/2) × 12j ((p(p2 - 1))/2) × 12j ((p(p2 - 1))/2) × 12j










































to end of page
to top of page