Bilbao Crystallographic Server arrow Wyckoff Sets: Equivalent Sets of Wyckoff Positions

Wyckoff Sets of Space Group P42/mmc (No. 131)

NOTE: The program uses the default choice for the group settings.

Letter Mult SS Rep. Equivalent WP
r 16 1 (x, y, z) r
q 8 m.. (x, y, 0) q
p 8 .m. (1/2 , y, z) op
o 8 .m. (0, y, z) op
n 8 ..2 (x, x, 1/4 ) n
m 4 m2m . (x, 1/2 , 0) jklm
l 4 m2m . (x, 0, 1/2 ) jklm
k 4 m2m . (x, 1/2 , 1/2 ) jklm
j 4 m2m . (x, 0, 0) jklm
i 4 2mm . (0, 1/2 , z) i
h 4 2mm . (1/2 , 1/2 , z) gh
g 4 2mm . (0, 0, z) gh
f 2 -4m2 (1/2 , 1/2 , 1/4 ) ef
e 2 -4m2 (0, 0, 1/4 ) ef
d 2 mmm . (0, 1/2 , 1/2 ) cd
c 2 mmm . (0, 1/2 , 0) cd
b 2 mmm . (1/2 , 1/2 , 0) ab
a 2 mmm . (0, 0, 0) ab

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P42/mmc (131) under the coset representatives of its affine normalizer


The affine normalizer coincides with the Euclidean one.

Index: 4

No. # Coset RepresentativeGeometrical Interpretation Transformed WP
1x,y,z
(
   1   0   0    0
   0   1   0    0
   0   0   1    0
)
1 
a b c d e f g h i j k l m n o p q r
2x+1/2,y+1/2,z
(
   1   0   0   1/2
   0   1   0   1/2
   0   0   1    0
)
t (1/2,1/2,0) 
b a d c f e h g i m l k j n p o q r
3x,y,z+1/2
(
   1   0   0    0
   0   1   0    0
   0   0   1   1/2
)
t (0,0,1/2) 
a b d c e f g h i l m j k n o p q r
4x+1/2,y+1/2,z+1/2
(
   1   0   0   1/2
   0   1   0   1/2
   0   0   1   1/2
)
t (1/2,1/2,1/2) 
b a c d f e h g i k j m l n p o q r


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