cm2e m2m Orthorhombic/Rectangular
No. 36 cm2e Patterson symmetry cmmm

symmetry group diagram

Origin on b2a

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

Symmetry of special projections

Along [001]   p1m1
a' = 1/2a   b' = 1/2b   
Origin at 0, 0, z
Along [100]   [script p]11m
a' = 1/2b   
Origin at x, 0, 0
Along [010]   [script p]2mg
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] c11a (p11a, 5) (1; 4)+
IIa [2] pb21a (33) 1; 4; (2; 3) + (1/21/2, 0)
  [2] pm2a (31) 1; 2; 3; 4
  [2] pb2b (30) 1; 2; (3; 4) + (1/21/2, 0)
  [2] pm21b (28) 1; 3; (2; 4) + (1/21/2, 0)
IIb none

Maximal isotypic subgroups of lowest index


IIc [3] cm2e (a' = 3a) (36); [3] cm2e (b' = 3b) (36)

Minimal non-isotypic supergroups


I [2] cmme (48)
II [2] pm2m (a' = 1/2ab' = 1/2b) (27)








































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