[script p]222 222 Orthorhombic
No. 13 [script p]222 Patterson symmetry [script p]mmm

symmetry group diagram

Origin at 222

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

Symmetry operations

(1)  1
      (1 | 0, 0, 0)
(2)  2   0, 0, z
      (2z | 0, 0, 0)
(3)  2   0, y, 0
      (2y | 0, 0, 0)
(4)  2   x, 0, 0
      (2x | 0, 0, 0)

Generators selected (1); t(0, 0, 1); (2); (3)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

 General:
4 h 1
(1) xyz(2) -x-yz(3) -xy-z(4) x-y-z
no conditions
  Special: no extra conditions
2 g  . . 2 
0, 0, z0, 0, -z
2 f  . 2 . 
0, y1/20, -y1/2
2 e  . 2 . 
0, y, 00, -y, 0
2 d  2 . . 
x, 0, 1/2-x, 0, 1/2
2 c  2 . . 
x, 0, 0-x, 0, 0
1 b  2 2 2 
0, 0, 1/2
1 a  2 2 2 
0, 0, 0

Symmetry of special projections

Along [001]   2mm

Origin at 0, 0, z
Along [100]   [script p]2mm
a' = c   
Origin at x, 0, 0
Along [010]   [script p]2mm
a' = c   
Origin at 0, y, 0

Maximal non-isotypic non-enantiomorphic subgroups


I[2] [script p]112 (8)1; 2
 [2] [script p]121 ([script p]211, 3)1; 3
 [2] [script p]211 (3)1; 4
IIa none
IIb[2] [script p]2221 (c' = 2c) (14)

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index


IIc[2] [script p]222 (c' = 2c) (13)

Minimal non-isotypic non-enantiomorphic supergroups


I[2] [script p]mmm (20); [2] [script p]ccm (21); [2] [script p]422 (30); [2] [script p]4222 (32); [2] [script p]-42m (37); [2] [script p]-42c (38); [3] [script p]622 (62); [3] [script p]6222 (64); [3] [script p]6422 (66)
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