pmam mmm Orthorhombic/Rectangular
No. 40 p21/m2/a2/m Patterson symmetry pmmm

symmetry group diagram

Origin at centre (2/m) at 21a2/m

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

Symmetry operations

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

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

Symmetry of special projections

Along [001]   p2mg
a' = a   b' = b   
Origin at 0, 0, z
Along [100]   [script p]2mm
a' = b   
Origin at x, 0, 0
Along [010]   [script p]2mm
a' = 1/2a   
Origin at 0, y, 0

Maximal non-isotypic subgroups


I [2] p21am (pb21m, 29) 1; 4; 6; 7
  [2] pm2m (27) 1; 2; 7; 8
  [2] pma2 (24) 1; 3; 6; 8
  [2] p2122 (20) 1; 2; 3; 4
  [2] p12/a1 (p2/b11, 16) 1; 2; 5; 6
  [2] p21/m11 (15) 1; 4; 5; 8
  [2] p112/m (6) 1; 3; 5; 7
IIa none
IIb [2] pmab (b' = 2b) (pbma, 45); [2] pbam (b' = 2b) (44); [2] pbab (b' = 2b) (pbaa, 43)

Maximal isotypic subgroups of lowest index


IIc [2] pmam (b' = 2b) (40); [3] pmam (a' = 3a) (40)

Minimal non-isotypic supergroups


I none
II [2] cmmm (47); [2] pmmm (b' = 1/2b) (37)








































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