c222 222 Orthorhombic/Rectangular
No. 22 c222 Patterson symmetry cmmm

symmetry group diagram

Origin at 222

Asymmetric unit 0 ≤ x ≤ 1/4; 0 ≤ y ≤ 1/2

Symmetry operations

For (0, 0, 0)+ set

(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)

For (1/21/2, 0)+ set

(1)  t (1/21/2, 0)  
      (1 | 1/21/2, 0)
(2)  2   1/41/4z
      (2z | 1/21/2, 0)
(3)  2 (0, 1/2, 0)   1/4y, 0
      (2y | 1/21/2, 0)
(4)  2 (1/2, 0, 0)   x1/4, 0
      (2x | 1/21/2, 0)

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(1/21/2, 0); (2); (3)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

  (0, 0, 0)+  (1/21/2, 0)+   General:
8 h 1
(1) xyz (2) -x-yz (3) -xy-z (4) x-y-z
hk: h + k = 2n
0k: k = 2n
h0: h = 2n
    Special: as above, plus
4 g  . . 2 
1/41/4z 3/41/4-z    
hk: h = 2n
4 f  . . 2 
0, 1/2z 0, 1/2-z    
no extra conditions
4 e  . . 2 
0, 0, z 0, 0, -z    
no extra conditions
4 d  . 2 . 
0, y, 0 0, -y, 0    
no extra conditions
4 c  2 . . 
x, 0, 0 -x, 0, 0    
no extra conditions
2 b  2 2 2 
0, 1/2, 0  
no extra conditions
2 a  2 2 2 
0, 0, 0  
no extra conditions

Symmetry of special projections

Along [001]   c2mm
a' = a   b' = b   
Origin at 0, 0, z
Along [100]   [script p]2mm
a' = 1/2b   
Origin at x, 0, 0
Along [010]   [script p]2mm
a' = 1/2a   
Origin at 0, y, 0

Maximal non-isotypic subgroups


I [2] c121 (c211, 10) (1; 3)+
  [2] c211 (10) (1; 4)+
  [2] c112 (p112, 3) (1; 2)+
IIa [2] p21212 (21) 1; 2; (3; 4) + (1/21/2, 0)
  [2] p2122 (20) 1; 3; (2; 4) + (1/21/2, 0)
  [2] p2212 (p2122, 20) 1; 4; (2; 3) + (1/21/2, 0)
  [2] p222 (19) 1; 2; 3; 4
IIb none

Maximal isotypic subgroups of lowest index


IIc [3] c222 (a' = 3a or b' = 3b) (22)

Minimal non-isotypic supergroups


I [2] cmmm (47); [2] cmme (48); [2] p422 (53); [2] p4212 (54); [2] p-4m2 (59); [2] p-4b2 (60); [3] p622 (76)
II [2] p222 (a' = 1/2ab' = 1/2b) (19)








































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