p2122 222 Orthorhombic/Rectangular
No. 20 p2122 Patterson symmetry pmmm

symmetry group diagram

Origin at 2112

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

Symmetry operations

(1)  1
      (1 | 0, 0, 0)
(2)  2 (1/2, 0, 0)   x, 0, 0
      (2x | 1/2, 0, 0)
(3)  2   1/4y, 0
      (2y | 1/2, 0, 0)
(4)  2   0, 0, z
      (2z | 0, 0, 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 d 1
(1) xyz (2) x + 1/2-y-z (3) -x + 1/2y-z (4) -x-yz
h0: h = 2n
    Special: as above, plus
2 c  . 2 . 
1/4y, 0 3/4-y, 0
no extra conditions
2 b  . . 2 
0, 1/2z 1/21/2-z
hk: h = 2n
2 a  . . 2 
0, 0, z 1/2, 0, -z
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]2mg
a' = a   
Origin at 1/4y, 0

Maximal non-isotypic subgroups


I [2] p2111 (9) 1; 2
  [2] p121 (p211, 8) 1; 3
  [2] p112 (3) 1; 4
IIa none
IIb [2] p21212 (b' = 2b) (21)

Maximal isotypic subgroups of lowest index


IIc [2] p2122 (b' = 2b) (20); [3] p2122 (a' = 3a) (20)

Minimal non-isotypic supergroups


I [2] pmam (40); [2] pmma (41); [2] pman (42); [2] pbaa (43); [2] pbma (45)
II [2] c222 (22); [2] p222 (a' = 1/2a) (19)








































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