cm2m m2m Orthorhombic/Rectangular
No. 35 cm2m Patterson symmetry cmmm

symmetry group diagram

Origin on m2m

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

Symmetry operations

For (0, 0, 0)+ set

(1)  1
      (1 | 0, 0, 0)
(2)  2   0, y, 0
      (2y | 0, 0, 0)
(3)  m   0, yz
      (mx | 0, 0, 0)
(4)  m   xy, 0
      (mz | 0, 0, 0)

For (1/21/2, 0)+ set

(1)  t (1/21/2, 0)  
      (1 | 1/21/2, 0)
(2)  2 (0, 1/2, 0)   1/4y, 0
      (2y | 1/21/2, 0)
(3)  b   1/4yz
      (mx | 1/21/2, 0)
(4)  n (1/21/2, 0)   xy, 0
      (mz | 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 d 1
(1) xyz (2) -xy-z (3) -xyz (4) xy-z
hk: h + k = 2n
h0: h = 2n
0k: k = 2n
    Special: no extra conditions
4 c  . . m 
xy, 0 -xy, 0    
4 b  m . . 
0, yz 0, y-z    
2 a  m 2 m 
0, y, 0  

Symmetry of special projections

Along [001]   c1m1
a' = a   b' = b   
Origin at 0, 0, z
Along [100]   [script p]11m
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] cm11 (13) (1; 3)+
  [2] c121 (c211, 10) (1; 2)+
  [2] c11m (p11m, 4) (1; 4)+
IIa [2] pb2n (34) 1; 2; (3; 4) + (1/21/2, 0)
  [2] pm21n (32) 1; 3; (2; 4) + (1/21/2, 0)
  [2] pb21m (29) 1; 4; (2; 3) + (1/21/2, 0)
  [2] pm2m (27) 1; 2; 3; 4
IIb none

Maximal isotypic subgroups of lowest index


IIc [3] cm2m (a' = 3a) (35); [3] cm2m (b' = 3b) (35)

Minimal non-isotypic supergroups


I [2] cmmm (47)
II [2] pm2m (a' = 1/2ab' = 1/2b) (27)








































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