pm2m m2m Orthorhombic/Rectangular
No. 27 pm2m Patterson symmetry pmmm

symmetry group diagram

Origin on m2m

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

Symmetry operations

(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)

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

  General:
4 f 1
(1) xyz (2) -xy-z (3) -xyz (4) xy-z
no conditions
    Special: no extra conditions
2 e  . . m 
xy, 0 -xy, 0
2 d  m . . 
1/2yz 1/2y-z
2 c  m . . 
0, yz 0, y-z
1 b  m 2 m 
1/2y, 0
1 a  m 2 m 
0, y, 0

Symmetry of special projections

Along [001]   p1m1
a' = a   b' = b   
Origin at 0, 0, z
Along [100]   [script p]11m
a' = b   
Origin at x, 0, 0
Along [010]   [script p]2mm
a' = a   
Origin at 0, y, 0

Maximal non-isotypic subgroups


I [2] pm11 (11) 1; 3
  [2] p121 (p211, 8) 1; 2
  [2] p11m (4) 1; 4
IIa none
IIb [2] cm2e (a' = 2ab' = 2b) (36); [2] cm2m (a' = 2ab' = 2b) (35); [2] pm2a (a' = 2a) (31); [2] pb2b (b' = 2b) (30); [2] pb21m (b' = 2b) (29); [2] pm21b (b' = 2b) (28)

Maximal isotypic subgroups of lowest index


IIc [2] pm2m (a' = 2a) (27); [2] pm2m (b' = 2b) (27)

Minimal non-isotypic supergroups


I [2] pmmm (37); [2] pmam (40); [3] p-6m2 (78); [3] p-62m (79)
II [2] cm2m (35)








































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