pb2b m2m Orthorhombic/Rectangular
No. 30 pb2b Patterson symmetry pmmm

symmetry group diagram

Origin on b2b

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

Symmetry operations

(1)  1
      (1 | 0, 0, 0)
(2)  2   0, y, 0
      (2y | 0, 0, 0)
(3)  b   xy, 0
      (mz | 0, 1/2, 0)
(4)  b   0, yz
      (mx | 0, 1/2, 0)

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

  General:
4 c 1
(1) xyz (2) -xy-z (3) xy + 1/2-z (4) -xy + 1/2z
hk: k = 2n
0k: k = 2n
    Special: no extra conditions
2 b  . 2 . 
1/2y, 0 1/2y + 1/2, 0
2 a  . 2 . 
0, y, 0 0, y + 1/2, 0

Symmetry of special projections

Along [001]   p1m1
a' = a   b' = 1/2b   
Origin at 0, 0, z
Along [100]   [script p]11m
a' = 1/2b   
Origin at x, 0, 0
Along [010]   [script p]2mm
a' = a   
Origin at 0, y, 0

Maximal non-isotypic subgroups


I [2] pb11 (12) 1; 4
  [2] p121 (p211, 8) 1; 2
  [2] p11b (p11a, 5) 1; 3
IIa none
IIb [2] pb2n (a' = 2a) (34)

Maximal isotypic subgroups of lowest index


IIc [2] pb2b (a' = 2a) (30); [3] pb2b (b' = 3b) (30)

Minimal non-isotypic supergroups


I [2] pmaa (38); [2] pbaa (43)
II [2] cm2e (36); [2] pm2m (b' = 1/2b) (27)








































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