pban mmm Orthorhombic/Rectangular
No. 39 p2/b2/a2/n Patterson symmetry pmmm

symmetry group diagram

Origin at -1 at ban, at -1/4, -1/4, 0 from 222

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

Symmetry operations

(1)  1
      (1 | 0, 0, 0)
(2)  2   1/41/4z
      (2z | 1/21/2, 0)
(3)  2   1/4y, 0
      (2y | 1/2, 0, 0)
(4)  2   x1/4, 0
      (2x | 0, 1/2, 0)
(5)  -1   0, 0, 0
      (-1 | 0, 0, 0)
(6)  n (1/21/2, 0)   xy, 0
      (mz | 1/21/2, 0)
(7)  a   x, 0, z
      (my | 1/2, 0, 0)
(8)  b   0, yz
      (mx | 0, 1/2, 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 h 1
(1) xyz (2) -x + 1/2-y + 1/2z (3) -x + 1/2y-z (4) x-y + 1/2-z
(5) -x-y-z (6) x + 1/2y + 1/2-z (7) x + 1/2-yz (8) -xy + 1/2z
hk: h + k = 2n
h0: h = 2n
0k: k = 2n
    Special: as above, plus
4 g  . . 2 
1/43/4z 1/43/4-z 3/41/4-z 3/41/4z
no extra conditions
4 f  . . 2 
1/41/4z 1/41/4-z 3/43/4-z 3/43/4z
no extra conditions
4 e  . 2 . 
1/4y, 0 1/4-y + 1/2, 0 3/4-y, 0 3/4y + 1/2, 0
no extra conditions
4 d  2 . . 
x1/4, 0 -x + 1/21/4, 0 -x3/4, 0 x + 1/23/4, 0
no extra conditions
4 c  -1 
0, 0, 0 1/21/2, 0 1/2, 0, 0 0, 1/2, 0
hk: hk = 2n
2 b  2 2 2 
3/41/4, 0 1/43/4, 0
no extra conditions
2 a  2 2 2 
1/41/4, 0 3/43/4, 0
no extra conditions

Symmetry of special projections

Along [001]   c2mm
a' = a   b' = b   
Origin at 1/41/4z
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] pb2n (34) 1; 3; 6; 8
  [2] p2an (pb2n, 34) 1; 4; 6; 7
  [2] pba2 (25) 1; 2; 7; 8
  [2] p222 (19) 1; 2; 3; 4
  [2] p12/a1 (p2/b11, 16) 1; 3; 5; 7
  [2] p2/b11 (16) 1; 4; 5; 8
  [2] p112/n (p112/a, 7) 1; 2; 5; 6
IIa none
IIb none

Maximal isotypic subgroups of lowest index


IIc [3] pban (a' = 3a or b' = 3b) (39)

Minimal non-isotypic supergroups


I [2] p4/nbm (62)
II [2] cmmm (47); [2] pmaa (b' = 1/2b) (38)








































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