p-4b2 -4m2 Tetragonal/Square
No. 60 p-4b2 Patterson symmetry p4/mmm

symmetry group diagram

Origin at -4121

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

Symmetry operations

(1)  1
      (1 | 0, 0, 0)
(2)  2   0, 0, z
      (2z | 0, 0, 0)
(3)  -4+   0, 0, z; 0, 0, 0
      (-4z | 0, 0, 0)
(4)  -4-   0, 0, z; 0, 0, 0
      (-4z-1 | 0, 0, 0)
(5)  a   x1/4z
      (my | 1/21/2, 0)
(6)  b   1/4yz
      (mx | 1/21/2, 0)
(7)  2 (1/21/2, 0)   xx, 0
      (2xy | 1/21/2, 0)
(8)  2   x-x+1/2, 0
      (2-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 f 1
(1) xyz (2) -x-yz (3) y-x-z (4) -yx-z
(5) x + 1/2-y + 1/2z (6) -x + 1/2y + 1/2z (7) y + 1/2x + 1/2-z (8) -y + 1/2-x + 1/2-z
h0: h = 2n
0k: k = 2n
    Special: as above, plus
4 e  . . 2 
xx + 1/2, 0 -x-x + 1/2, 0 x + 1/2-x, 0 -x + 1/2x, 0
no extra conditions
4 d  2 . . 
0, 1/2z 1/2, 0, -z 1/2, 0, z 0, 1/2-z
hk: h + k = 2n
4 c  2 . . 
0, 0, z 0, 0, -z 1/21/2z 1/21/2-z
hk: h + k = 2n
2 b  2 . 22 
0, 1/2, 0 1/2, 0, 0
hk: h + k = 2n
2 a  -4 . . 
0, 0, 0 1/21/2, 0
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]2mm
a' = 1/2(-a + b)   
Origin at xx, 0

Maximal non-isotypic subgroups


I [2] p-411 (p-4, 50) 1; 2; 3; 4
  [2] p2b1 (pba2, 25) 1; 2; 5; 6
  [2] p212 (c222, 22) 1; 2; 7; 8
IIa none
IIb none

Maximal isotypic subgroups of lowest index


IIc [9] p-4b2 (a' = 3ab' = 3b) (60)

Minimal non-isotypic supergroups


I [2] p4/nbm (62); [2] p4/mbm (63)
II [2] c-4m2 (p-42m, 57)








































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