pmm2 mm2 Orthorhombic/Rectangular
No. 23 pmm2 Patterson symmetry pmmm

symmetry group diagram

Origin on mm2

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

Symmetry operations

(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)

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

  General:
4 i 1
(1) xyz (2) -x-yz (3) x-yz (4) -xyz
no conditions
    Special: no extra conditions
2 h  m . . 
1/2yz 1/2-yz
2 g  m . . 
0, yz 0, -yz
2 f  . m . 
x1/2z -x1/2z
2 e  . m . 
x, 0, z -x, 0, z
1 d  m m 2 
1/21/2z
1 c  m m 2 
1/2, 0, z
1 b  m m 2 
0, 1/2z
1 a  m m 2 
0, 0, z

Symmetry of special projections

Along [001]   p2mm
a' = a   b' = b   
Origin at 0, 0, z
Along [100]   [script p]1m1
a' = b   
Origin at x, 0, 0
Along [010]   [script p]1m1
a' = a   
Origin at 0, y, 0

Maximal non-isotypic subgroups


I [2] p1m1 (pm11, 11) 1; 3
  [2] pm11 (11) 1; 4
  [2] p112 (3) 1; 2
IIa none
IIb [2] cmm2 (a' = 2ab' = 2b) (26); [2] pma2 (a' = 2a) (24); [2] pbm2 (b' = 2b) (pma2, 24)

Maximal isotypic subgroups of lowest index


IIc [2] pmm2 (a' = 2a or b' = 2b) (23)

Minimal non-isotypic supergroups


I [2] pmmm (37); [2] pmma (41); [2] pmmn (46); [2] p4mm (55); [2] p-4m2 (59)
II [2] cmm2 (26)








































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