p21212 222 Orthorhombic/Rectangular
No. 21 p21212 Patterson symmetry pmmm

symmetry group diagram

Origin at intersection of 2 with perpendicular plane containing 21 axes

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

Symmetry operations

(1)  1
      (1 | 0, 0, 0)
(2)  2   0, 0, z
      (2z | 0, 0, 0)
(3)  2 (0, 1/2, 0)   1/4y, 0
      (2y | 1/21/2, 0)
(4)  2 (1/2, 0, 0)   x1/4, 0
      (2x | 1/21/2, 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) -x-yz (3) -x + 1/2y + 1/2-z (4) x + 1/2-y + 1/2-z
h0: h = 2n
0k: k = 2n
    Special: as above, plus
2 b  . . 2 
0, 1/2z 1/2, 0, -z
hk: h + k = 2n
2 a  . . 2 
0, 0, z 1/21/2-z
hk: h + k = 2n

Symmetry of special projections

Along [001]   p2gg
a' = a   b' = b   
Origin at 0, 0, z
Along [100]   [script p]2mg
a' = b   
Origin at x1/4, 0
Along [010]   [script p]2mg
a' = a   
Origin at 1/4y, 0

Maximal non-isotypic subgroups


I [2] p1211 (p2111, 9) 1; 3
  [2] p2111 (9) 1; 4
  [2] p112 (3) 1; 2
IIa none
IIb none

Maximal isotypic subgroups of lowest index


IIc [3] p21212 (a' = 3a or b' = 3b) (21)

Minimal non-isotypic supergroups


I [2] pbam (44); [2] pmmn (46); [2] p4212 (54); [2] p-421m (58)
II [2] c222 (22); [2] p2212 (a' = 1/2a) (p2122, 20)








































to end of page
to top of page