P622 No. 177 D61


Axes Coordinates Wyckoff positions
1a 1b 2c 2d 2e 3f 3g
4h 6i 6j 6k 6l 6m 12n
I Maximal translationengleiche subgroups
[2] P6 (168) 1a 1a 2b 2b 2 × 1a 3c 3c
2 × 2b 2 × 3c 6d 6d 6d 6d 2 × 6d
[2] P321 1a 1b 2d 2d 2c 3e 3f
  (150) 2 × 2d 6g 2 × 3e 2 × 3f 6g 6g 2 × 6g
[2] P312 1a 1b 1c; 1e 1d; 1f 2g 3j 3k
  (149) 2h; 2i 6l 6l 6l 2 × 3j 2 × 3k 2 × 6l
[3] C222 a, a + 2b, c x - (1/2)y, (1/2)y, z 2a 2d 4g 4h 4i 2b; 4k 2c; 4k
  (21) 8l 4j; 2 × 4k 4e; 8l 4f; 8l 4g; 8l 4h; 8l 3 × 8l
 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] P6322 a, b, 2c x, y, (1/2)z; 2a 2b 4f 2c; 2d 4e 6g 6h
  (182) +(0, 0, (1/2)) 2 × 4f 12i 2 × 6g 12i 12i 2 × 6h 2 × 12i
[2] P6322 a, b, 2c x, y, (1/2)z + (1/4); 2b 2a 2c; 2d 4f 4e 6h 6g
  (182) +(0, 0, (1/2)) 2 × 4f 12i 12i 2 × 6g 2 × 6h 12i 2 × 12i
[3] P6422 a, b, 3c x, y, (1/3)z; 3a 3b 6i 6j 6e 3c; 6f 3d; 6f
  (181) ±(0, 0, (1/3)) 12k 3 × 6f 6g; 12k 6h; 12k 6i; 12k 6j; 12k 3 × 12k
[3] P6222 a, b, 3c x, y, (1/3)z; 3a 3b 6i 6j 6e 3c; 6f 3d; 6f
  (180) ±(0, 0, (1/3)) 12k 3 × 6f 6g; 12k 6h; 12k 6i; 12k 6j; 12k 3 × 12k
   Enlarged unit cell, isomorphic
[2] P622 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 12n 2 × 12n
[2] P622 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 12n 6l; 6m 2 × 12n
[3] P622 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; 12n 6m; 12n 3 × 12n
[p] P622 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) × 12n 6m; ((p - 1)/2) × 12n p × 12n
p = prime > 2;
u = 1, . . ., p - 1
[3] P622 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; 12n 3 × 6l 3 × 6m 6j; 12n 6k; 12n 3 × 12n
±((1/3), (2/3), 0)
[4] P622 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; 12n 2 × 12n 2 × 6j; 12n 2 × 6k; 12n 2 × 6l; 12n 2 × 6m; 12n 4 × 12n
+(0, (1/2), 0); +((1/2), (1/2), 0)
[p2] P622 pa, pb, c (1/p)x, (1/p)y, z; 1a; ((p - 1)/2) × 6j; 1b; ((p - 1)/2) × 6k; 2c; 2d; 2e; ((p2 - 1)/6) × 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) × 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)2)/4) × 12n (((p - 1)2)/4) × 12n
u, v = 1, . . ., p - 1 12n 12n 12n 12n
4h; 6i; p × 6j; p × 6k; p × 6l; p × 6m; p2 × 12n
((p2 - 1)/3) × 12n ((p2 - 1)/2) × 12n ((p(p - 1))/2) × 12n ((p(p - 1))/2) × 12n ((p(p - 1))/2) × 12n ((p(p - 1))/2) × 12n









































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