pbaa mmm Orthorhombic/Rectangular
No. 43 p2/b21/a2/a Patterson symmetry pmmm

symmetry group diagram

Origin at -1 on b1a

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

Symmetry operations

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

Maximal non-isotypic subgroups


I [2] pb21a (33) 1; 4; 6; 7
  [2] p2aa (pb2b, 30) 1; 2; 7; 8
  [2] pba2 (25) 1; 3; 6; 8
  [2] p2212 (p2122, 20) 1; 2; 3; 4
  [2] p121/a1 (p21/b11, 17) 1; 4; 5; 8
  [2] p2/b11 (16) 1; 2; 5; 6
  [2] p112/a (7) 1; 3; 5; 7
IIa none
IIb none

Maximal isotypic subgroups of lowest index


IIc [3] pbaa (a' = 3a) (43); [3] pbaa (b' = 3b) (43)

Minimal non-isotypic supergroups


I none
II [2] cmme (48); [2] pmaa (b' = 1/2b) (38); [2] pmam (b' = 1/2b) (40)








































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