pm21n m2m Orthorhombic/Rectangular
No. 32 pm21n Patterson symmetry pmmm

symmetry group diagram

Origin on m1n

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

Symmetry operations

(1)  1
      (1 | 0, 0, 0)
(2)  2 (0, 1/2, 0)   1/4y, 0
      (2y | 1/21/2, 0)
(3)  n (1/21/2, 0)   xy, 0
      (mz | 1/21/2, 0)
(4)  m   0, yz
      (mx | 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 b 1
(1) xyz (2) -x + 1/2y + 1/2-z (3) x + 1/2y + 1/2-z (4) -xyz
hk: h + k = 2n
h0: h = 2n
0k: k = 2n
    Special: no extra conditions
2 a  m . . 
0, yz 1/2y + 1/2-z

Symmetry of special projections

Along [001]   c1m1
a' = a   b' = b   
Origin at 0, 0, z
Along [100]   [script p]11g
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] pm11 (11) 1; 4
  [2] p1211 (p2111, 9) 1; 2
  [2] p11n (p11a, 5) 1; 3
IIa none
IIb none

Maximal isotypic subgroups of lowest index


IIc [3] pm21n (a' = 3a) (32); [3] pm21n (b' = 3b) (32)

Minimal non-isotypic supergroups


I [2] pman (42); [2] pmmn (46)
II [2] cm2m (35); [2] pm21b (a' = 1/2a) (28); [2] pm2a (b' = 1/2b) (31)








































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