pmma mmm Orthorhombic/Rectangular
No. 41 p21/m2/m2/a Patterson symmetry pmmm

symmetry group diagram

Origin at centre (2/m) at 212/ma

Asymmetric unit 0 ≤ x ≤ 1/4; 0 ≤ y ≤ 1/2

Symmetry operations

(1)  1    (2)  2   1/4, 0, z (3)  2   0, y, 0 (4)  2(1/2, 0, 0)   x, 0, 0
(5)  -1   0, 0, 0 (6)  a   xy, 0 (7)  m   x, 0, z (8)  m   1/4yz

Generators selected (1); t(1, 0, 0); t(0, 1, 0); (2); (3); (5)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

  General:
8 i 1
(1) xyz (2) -x + 1/2-yz (3) -xy-z (4) x + 1/2-y-z
(5) -x-y-z (6) x + 1/2y-z (7) x-yz (8) -x + 1/2yz
hk: h = 2n
h0: h = 2n
    Special: no extra conditions
4 h  m . . 
1/4yz 1/4-yz 3/4y-z 3/4-y-z
4 g  . m . 
x1/2z -x + 1/21/2z -x1/2-z x + 1/21/2-z
4 f  . m . 
x, 0, z -x + 1/2, 0, z -x, 0, -z x + 1/2, 0, -z
4 e  . 2 . 
0, y, 0 1/2-y, 0 0, -y, 0 1/2y, 0
2 d  m m 2 
1/41/2z 3/41/2-z
2 c  m m 2 
1/4, 0, z 3/4, 0, -z
2 b  . 2/m . 
0, 1/2, 0 1/21/2, 0
2 a  . 2/m . 
0, 0, 0 1/2, 0, 0

Symmetry of special projections

Along [001]   p2mm
a' = 1/2a   b' = b   
Origin at 0, 0, z
Along [100]   [script p]2mm
a' = b   
Origin at x, 0, 0
Along [010]   [script p]2mg
a' = a   
Origin at 0, y, 0

Maximal non-isotypic subgroups


I [2] pm2a (31) 1; 3; 6; 8
  [2] p21ma (pm21b, 28) 1; 4; 6; 7
  [2] pmm2 (23) 1; 2; 7; 8
  [2] p2122 (20) 1; 2; 3; 4
  [2] p21/m11 (15) 1; 4; 5; 8
  [2] p12/m1 (p2/m11, 14) 1; 3; 5; 7
  [2] p112/a (7) 1; 2; 5; 6
IIa none
IIb [2] pmmn (b' = 2b) (46); [2] pbma (b' = 2b) (45); [2] pbmn (b' = 2b) (pman, 42)

Maximal isotypic subgroups of lowest index


IIc [2] pmma (b' = 2b) (41); [3] pmma (a' = 3a) (41)

Minimal non-isotypic supergroups


I none
II [2] cmme (48); [2] pmmm (b' = 1/2b) (37)








































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