cmm2 mm2 Orthorhombic/Rectangular
No. 26 cmm2 Patterson symmetry cmmm

symmetry group diagram

Origin on mm2

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)  m   x, 0, z
      (my | 0, 0, 0)
(4)  m   0, yz
      (mx | 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)  a   x1/4z
      (my | 1/21/2, 0)
(4)  b   1/4yz
      (mx | 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 f 1
(1) xyz (2) -x-yz (3) x-yz (4) -xyz
hk: h + k = 2n
0k: k = 2n
h0: h = 2n
    Special: as above, plus
4 e  m . . 
0, yz 0, -yz    
no extra conditions
4 d  . m . 
x, 0, z -x, 0, z    
no extra conditions
4 c  . . 2 
1/41/4z 1/43/4z    
hk: h = 2n
2 b  m m 2 
0, 1/2z  
no extra conditions
2 a  m m 2 
0, 0, z  
no extra conditions

Symmetry of special projections

Along [001]   c2mm
a' = a   b' = b   
Origin at 0, 0, z
Along [100]   [script p]1m1
a' = 1/2b   
Origin at x, 0, 0
Along [010]   [script p]1m1
a' = 1/2a   
Origin at 0, y, 0

Maximal non-isotypic subgroups


I [2] c1m1 (cm11, 13) (1; 3)+
  [2] cm11 (13) (1; 4)+
  [2] c112 (p112, 3) (1; 2)+
IIa [2] pba2 (25) 1; 2; (3; 4) + (1/21/2, 0)
  [2] pbm2 (pma2, 24) 1; 3; (2; 4) + (1/21/2, 0)
  [2] pma2 (24) 1; 4; (2; 3) + (1/21/2, 0)
  [2] pmm2 (23) 1; 2; 3; 4
IIb none

Maximal isotypic subgroups of lowest index


IIc [3] cmm2 (a' = 3a or b' = 3b) (26)

Minimal non-isotypic supergroups


I [2] cmmm (47); [2] cmme (48); [2] p4mm (55); [2] p4bm (56); [2] p-42m (57); [2] p-421m (58); [3] p6mm (77)
II [2] pmm2 (a' = 1/2ab' = 1/2b) (23)








































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