[script p]-62m -62m Hexagonal
No. 71 [script p]-62m Patterson symmetry [script p]6/mmm
SECOND SETTING

symmetry group diagram

Origin on -62m

Asymmetric unit 0 ≤ x; 0 ≤ y; 0 ≤ z ≤ 1/2; y ≤ x

Symmetry operations

(1)  1   (2)  3+   0, 0, z(3)  3-   0, 0, z
(4)  m   xy, 0(5)  -6-   0, 0, z; 0, 0, 0(6)  -6+   0, 0, z; 0, 0, 0
(7)  2   xx, 0(8)  2   x, 0, 0(9)  2   0, y, 0
(10)  m   xxz(11)  m   x, 0, z(12)  m   0, yz

Generators selected (1); t(0, 0, 1); (2); (4); (7)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

 General:
12 i 1
(1) xyz(2) -yx - yz(3) -x + y-xz
(4) xy-z(5) -yx - y-z(6) -x + y-x-z
(7) yx-z(8) x - y-y-z(9) -x-x + y-z
(10) yxz(11) x - y-yz(12) -x-x + yz
no conditions
  Special: no extra conditions
6 h  m . . 
xy1/2-yx - y1/2-x + y-x1/2yx1/2x - y-y1/2-x-x + y1/2
6 g  m . . 
xy, 0-yx - y, 0-x + y-x, 0yx, 0x - y-y, 0-x-x + y, 0
6 f  . . m 
x, 0, z0, xz-x-xzx, 0, -z0, x-z-x-x-z
3 e  m 2 m 
x, 0, 1/20, x1/2-x-x1/2
3 d  m 2 m 
x, 0, 00, x, 0-x-x, 0
2 c  3 . m 
0, 0, z0, 0, -z
1 b  -6 2 m 
0, 0, 1/2
1 a  -6 2 m 
0, 0, 0

Symmetry of special projections

Along [001]   3m

Origin at 0, 0, z
Along [100]   [script p]2mm
a' = c   
Origin at x, 0, 0
Along [210]   [script p]1m1
a' = c   
Origin at x1/2x, 0

Maximal non-isotypic non-enantiomorphic subgroups


I[2] [script p]-611 ([script p]-6, 59)1; 2; 3; 4; 5; 6
 [2] [script p]31m ([script p]3m1, 49)1; 2; 3; 10; 11; 12
 [2] [script p]321 ([script p]312, 46)1; 2; 3; 7; 8; 9
 [3] [script p]m2m ([script p]2mm, 18)1; 4; 7; 10
 [3] [script p]m2m ([script p]2mm, 18)1; 4; 8; 11
 [3] [script p]m2m ([script p]2mm, 18)1; 4; 9; 12
IIa none
IIb[2] [script p]-62c (c' = 2c) ([script p]-6c2, 72)

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index


IIc[2] [script p]-62m (c' = 2c) ([script p]-6m2, 71)

Minimal non-isotypic non-enantiomorphic supergroups


I[2] [script p]6/mmm (73); [2] [script p]63/mmc (75)
IInone








































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