P6/mmm No. 191 P6/m2/m2/m D6h1


Axes Coordinates Wyckoff positions
1a 1b 2c 2d 2e 3f 3g 4h 6i 6j 6k 6l 6m
12n 12o 12p 12q 24r
I Maximal translationengleiche subgroups
[2] P-62m (189) 1a 1b 2c 2d 2e 3f 3g 4h 6i 2 × 3f 2 × 3g 6j 6k
2 × 6i 12l 2 × 6j 2 × 6k 2 × 12l
[2] P-6m2 (187) 1a 1b 1c; 1e 1d; 1f 2g 3j 3k 2h; 2i 6n 6l 6m 2 × 3j 2 × 3k
12o 2 × 6n 2 × 6l 2 × 6m 2 × 12o
[2] P6mm (183) 1a 1a 2b 2b 2 × 1a 3c 3c 2 × 2b 2 × 3c 6d 6d 6e 6e
2 × 6d 2 × 6e 12f 12f 2 × 12f
[2] P622 (177) 1a 1b 2c 2d 2e 3f 3g 4h 6i 6j 6k 6l 6m
12n 12n 12n 12n 2 × 12n
[2] P6/m (175) 1a 1b 2c 2d 2e 3f 3g 4h 6i 6j 6k 6j 6k
12l 12l 2 × 6j 2 × 6k 2 × 12l
[2] P-3m1 (164) 1a 1b 2d 2d 2c 3e 3f 2 × 2d 6i 6g 6h 6i 6i
12j 2 × 6i 12j 12j 2 × 12j
[2] P-31m (162) 1a 1b 2c 2d 2e 3f 3g 4h 6k 6k 6k 6i 6j
2 × 6k 12l 12l 12l 2 × 12l
[3] Cmmm a, a + 2b, c x - (1/2)y, (1/2)y, z 2a 2d 4i 4j 4k 2b; 4e 2c; 4f 8n 4l; 8m 4g; 8p 4h; 8q 4i; 8p 4j; 8q
  (65) 8o; 16r 8n; 16r 3 × 8p 3 × 8q 3 × 16r
 conjugate: b, -2a - b, c -(1/2)x + y, -(1/2)x, z
 conjugate: -a - b, a - b, c -(1/2)(x + y), (1/2)(x - y), z
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[2] P63/mmc a, b, 2c x, y, (1/2)z; 2a 2b 4f 2c; 2d 4e 6g 6h 2 × 4f 12k 12i 12j 12k 2 × 6h
  (194) +(0, 0, (1/2)) 24l 2 × 12k 24l 2 × 12j 2 × 24l
[2] P63/mmc a, b, 2c x, y, (1/2)z + (1/4); 2b 2a 2c; 2d 4f 4e 6h 6g 2 × 4f 12k 12j 12i 2 × 6h 12k
  (194) +(0, 0, (1/2)) 24l 2 × 12k 2 × 12j 24l 2 × 24l
[2] P63/mcm a, b, 2c x, y, (1/2)z; 2b 2a 4d 4c 4e 6f 6g 8h 12k 12k 2 × 6g 12i 12j
  (193) +(0, 0, (1/2)) 2 × 12k 24l 24l 2 × 12j 2 × 24l
[2] P63/mcm a, b, 2c x, y, (1/2)z + (1/4); 2a 2b 4c 4d 4e 6g 6f 8h 12k 2 × 6g 12k 12j 12i
  (193) +(0, 0, (1/2)) 2 × 12k 24l 2 × 12j 24l 2 × 24l
[2] P6/mcc a, b, 2c x, y, (1/2)z; 2b 2a 4d 4c 4e 6g 6f 8h 12i 12l 12j 12l 12k
  (192) +(0, 0, (1/2)) 24m 24m 2 × 12l 24m 2 × 24m
[2] P6/mcc a, b, 2c x, y, (1/2)z + (1/4); 2a 2b 4c 4d 4e 6f 6g 8h 12i 12j 12l 12k 12l
  (192) +(0, 0, (1/2)) 24m 24m 24m 2 × 12l 2 × 24m


Axes Coordinates Wyckoff positions
1a 1b 2c 2d 2e 3f 3g
4h 6i 6j 6k 6l 6m
12n 12o 12p 12q 24r
   Enlarged unit cell, isomorphic
[2] P6/mmm a, b, 2c x, y, (1/2)z; 1a; 1b 2e 2c; 2d 4h 2 × 2e 3f; 3g 6i
+(0, 0, (1/2)) 2 × 4h 2 × 6i 6j; 6k 12n 6l; 6m 12o
2 × 12n 2 × 12o 12p; 12q 24r 2 × 24r
[2] P6/mmm a, b, 2c x, y, (1/2)z + (1/4); 2e 1a; 1b 4h 2c; 2d 2 × 2e 6i 3f; 3g
+(0, 0, (1/2)) 2 × 4h 2 × 6i 12n 6j; 6k 12o 6l; 6m
2 × 12n 2 × 12o 24r 12p; 12q 2 × 24r
[3] P6/mmm a, b, 3c x, y, (1/3)z; 1a; 2e 1b; 2e 2c; 4h 2d; 4h 3 × 2e 3f; 6i 3g; 6i
±(0, 0, (1/3)) 3 × 4h 3 × 6i 6j; 12n 6k; 12n 6l; 12o 6m; 12o
3 × 12n 3 × 12o 12p; 24r 12q; 24r 3 × 24r
[p] P6/mmm a, b, pc x, y, (1/p)z; 1a; ((p - 1)/2) × 2e 1b; ((p - 1)/2) × 2e 2c; ((p - 1)/2) × 4h 2d; ((p - 1)/2) × 4h p × 2e 3f; ((p - 1)/2) × 6i 3g; ((p - 1)/2) × 6i
+(0, 0, (u/p)) p × 4h p × 6i 6j; ((p - 1)/2) × 12n 6k; ((p - 1)/2) × 12n 6l; ((p - 1)/2) × 12o 6m; ((p - 1)/2) × 12o
p = prime > 2; u = 1, . . ., p - 1 p × 12n p × 12o 12p; ((p - 1)/2) × 24r 12q; ((p - 1)/2) × 24r p × 24r
[3] P6/mmm 2a + b, (1/3)(x + y), 1a; 2c 1b; 2d 6j 6k 2e; 4h 3f; 6l 3g; 6m
-a + b, c (1/3)(-x + 2y), z; 12n 6i; 12o 3 × 6l 3 × 6m 6j; 12p 6k; 12q
±((1/3), (2/3), 0) 3 × 12o 12n; 24r 3 × 12p 3 × 12q 3 × 24r
[4] P6/mmm 2a, 2b, c (1/2)x, (1/2)y, z; 1a; 3f 1b; 3g 2c; 6l 2d; 6m 2e; 6i 6j; 6l 6k; 6m
+((1/2), 0, 0); 4h; 12o 12n; 12o 2 × 6j; 12p 2 × 6k; 12q 2 × 6l; 12p 2 × 6m; 12q
+(0, (1/2), 0); +((1/2), (1/2), 0) 2 × 12n; 24r 2 × 12o; 24r 4 × 12p 4 × 12q 4 × 24r
[p2] P6/mmm pa, pb, c (1/p)x, (1/p)y, z; 1a; ((p - 1)/2) × 6j; 1b; ((p - 1)/2) × 6k; 2c; 2d; 2e; ((p - 1)/2) × 12n; 3f; ((p - 1)/2) × 6j; 3g; ((p - 1)/2) × 6k
+((u/p), (v/p), 0) ((p - 1)/2) × 6l; ((p - 1)/2) × 6m; (p - 1) × 6l; (p - 1) × 6m; ((p - 1)/2) × 12o; ((p - 1)/2) × 6l; ((p - 1)/2) × 6m;
p = prime > 4; (((p - 1)(p - 5))/12) × (((p - 1)(p - 5))/12) × (((p - 1)(p - 2))/6) × (((p - 1)(p - 2))/6) × (((p - 1)(p - 5))/12) × (((p - 1)2)/4) × 12p (((p - 1)2)/4) × 12q
u, v = 1, . . ., p - 1 12p 12p 12p 12p 24r
4h; 6i; ((p - 1)/2) × 12n; p × 6j; p × 6k; p × 6l; p × 6m;
(p - 1) × 12o; ((p - 1)/2) × 12o; ((p(p - 1))/2) × 12p ((p(p - 1))/2) × 12q ((p(p - 1))/2) × 12p ((p(p - 1))/2) × 12q
(((p - 1)(p - 2))/6) × (((p - 1)2)/4) × 24r
24r
p × 12n; p × 12o; p2 × 12p p2 × 12q p2 × 24r
((p(p - 1))/2) × 24r ((p(p - 1))/2) × 24r










































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