pmmn mmm Orthorhombic/Rectangular
No. 46 p21/m21/m2/n Patterson symmetry pmmm

symmetry group diagram

Origin at -1 on 2121n

Asymmetric unit 0 ≤ x ≤ 1/4; 0 ≤ y ≤ 1/2

Symmetry operations

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

Symmetry of special projections

Along [001]   c2mm
a' = a   b' = b   
Origin at 1/41/4z
Along [100]   [script p]2mg
a' = b   
Origin at x, 0, 0
Along [010]   [script p]2mg
a' = a   
Origin at 0, y, 0

Maximal non-isotypic subgroups


I [2] pm21n (32) 1; 3; 6; 8
  [2] p21mn (pm21n, 32) 1; 4; 6; 7
  [2] pmm2 (23) 1; 2; 7; 8
  [2] p21212 (21) 1; 2; 3; 4
  [2] p121/m1 (p21/m11, 15) 1; 3; 5; 7
  [2] p21/m11 (15) 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] pmmn (a' = 3a or b' = 3b) (46)

Minimal non-isotypic supergroups


I [2] p4/nmm (64)
II [2] cmmm (47); [2] pmma (b' = 1/2b) (41)








































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