p4bm 4mm Tetragonal/Square
No. 56 p4bm Patterson symmetry p4/mmm

symmetry group diagram

Origin on 41g

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

Symmetry operations

(1)  1
      (1 | 0, 0, 0)
(2)  2   0, 0, z
      (2z | 0, 0, 0)
(3)  4+   0, 0, z
      (4z | 0, 0, 0)
(4)  4-   0, 0, z
      (4z-1 | 0, 0, 0)
(5)  a   x1/4z
      (my | 1/21/2, 0)
(6)  b   1/4yz
      (mx | 1/21/2, 0)
(7)  m   x+1/2-xz
      (mxy | 1/21/2, 0)
(8)  g (1/21/2, 0)   xxz
      (m-xy | 1/21/2, 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 d 1
(1) xyz (2) -x-yz (3) -yxz (4) y-xz
(5) x + 1/2-y + 1/2z (6) -x + 1/2y + 1/2z (7) -y + 1/2-x + 1/2z (8) y + 1/2x + 1/2z
0k: k = 2n
h0: h = 2n
    Special: as above, plus
4 c  . . m 
xx + 1/2z -x-x + 1/2z -x + 1/2xz x + 1/2-xz
no extra conditions
2 b  2 . mm 
1/2, 0, z 0, 1/2z
hk: h + k = 2n
2 a  4 . . 
0, 0, z 1/21/2z
hk: h + k = 2n

Symmetry of special projections

Along [001]   p4gm
a' = a   b' = b   
Origin at 0, 0, z
Along [100]   [script p]1m1
a' = 1/2b   
Origin at x, 0, 0
Along [110]   [script p]1m1
a' = 1/2(-a + b)   
Origin at xx, 0

Maximal non-isotypic subgroups


I [2] p411 (p4, 49) 1; 2; 3; 4
  [2] p21m (cmm2, 26) 1; 2; 7; 8
  [2] p2b1 (pba2, 25) 1; 2; 5; 6
IIa none
IIb none

Maximal isotypic subgroups of lowest index


IIc [9] p4bm (a' = 3ab' = 3b) (56)

Minimal non-isotypic supergroups


I [2] p4/nbm (62); [2] p4/mbm (63)
II [2] c4mm (p4mm, 55)








































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