p-4m2 -4m2 Tetragonal/Square
No. 59 p-4m2 Patterson symmetry p4/mmm

symmetry group diagram

Origin at -4m2

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)  m   x, 0, z
      (my | 0, 0, 0)
(6)  m   0, yz
      (mx | 0, 0, 0)
(7)  2   xx, 0
      (2xy | 0, 0, 0)
(8)  2   x-x, 0
      (2-xy | 0, 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 i 1
(1) xyz (2) -x-yz (3) y-x-z (4) -yx-z
(5) x-yz (6) -xyz (7) yx-z (8) -y-x-z
no conditions
    Special:
4 h  . m . 
x1/2z -x1/2z 1/2-x-z 1/2x-z
no extra conditions
4 g  . m . 
x, 0, z -x, 0, z 0, -x-z 0, x-z
no extra conditions
4 f  . . 2 
xx, 0 -x-x, 0 x-x, 0 -xx, 0
no extra conditions
2 e  2 mm . 
0, 1/2z 1/2, 0, -z
hk: h + k = 2n
2 d  2 mm . 
1/21/2z 1/21/2-z
no extra conditions
2 c  2 mm . 
0, 0, z 0, 0, -z
no extra conditions
1 b  -4 m 2 
1/21/2, 0
no extra conditions
1 a  -4 m 2 
0, 0, 0
no extra conditions

Symmetry of special projections

Along [001]   p4mm
a' = a   b' = b   
Origin at 0, 0, z
Along [100]   [script p]1m1
a' = b   
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] p2m1 (pmm2, 23) 1; 2; 5; 6
  [2] p212 (c222, 22) 1; 2; 7; 8
IIa none
IIb [2] c-4m21 (a' = 2ab' = 2b) (p-421m, 58); [2] c-4m2 (a' = 2ab' = 2b) (p-42m, 57)

Maximal isotypic subgroups of lowest index


IIc [9] p-4m2 (a' = 3ab' = 3b) (59)

Minimal non-isotypic supergroups


I [2] p4/mmm (61); [2] p4/nmm (64)
II [2] c-4m2 (p-42m, 57)








































to end of page
to top of page