pbma mmm Orthorhombic/Rectangular
No. 45 p21/b21/m2/a Patterson symmetry pmmm

symmetry group diagram

Origin at -1 on 121a

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

Symmetry operations

(1)  1
      (1 | 0, 0, 0)
(2)  2 (0, 1/2, 0)   0, y, 0
      (2y | 0, 1/2, 0)
(3)  2 (1/2, 0, 0)   x1/4, 0
      (2x | 1/21/2, 0)
(4)  2   1/4, 0, z
      (2z | 1/2, 0, 0)
(5)  -1   0, 0, 0
      (-1 | 0, 0, 0)
(6)  m   x1/4z
      (my | 0, 1/2, 0)
(7)  b   1/4yz
      (mx | 1/21/2, 0)
(8)  a   xy, 0
      (mz | 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 d 1
(1) xyz (2) -xy + 1/2-z (3) x + 1/2-y + 1/2-z (4) -x + 1/2-yz
(5) -x-y-z (6) x-y + 1/2z (7) -x + 1/2y + 1/2z (8) x + 1/2y-z
hk: h = 2n
h0: h = 2n
0k: k = 2n
    Special: as above, plus
4 c  . m . 
x1/4z -x3/4-z x + 1/21/4-z -x + 1/23/4z
no extra conditions
4 b  . . 2 
1/4, 0, z 3/41/2-z 3/4, 0, -z 1/41/2z
hk: k = 2n
4 a  -1 
0, 0, 0 0, 1/2, 0 1/21/2, 0 1/2, 0, 0
hk: k = 2n

Symmetry of special projections

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

Maximal non-isotypic subgroups


I [2] pb21a (33) 1; 2; 7; 8
  [2] p21ma (pm21b, 28) 1; 3; 6; 8
  [2] pbm2 (pma2, 24) 1; 4; 6; 7
  [2] p21212 (21) 1; 2; 3; 4
  [2] p21/b11 (17) 1; 3; 5; 7
  [2] p121/m1 (p21/m11, 15) 1; 2; 5; 6
  [2] p112/a (7) 1; 4; 5; 8
IIa none
IIb none

Maximal isotypic subgroups of lowest index


IIc [3] pbma (a' = 3a) (45); [3] pbma (b' = 3b) (45)

Minimal non-isotypic supergroups


I none
II [2] cmme (48); [2] pmam (b' = 1/2b) (40); [2] pmma (b' = 1/2b) (41)








































to end of page
to top of page