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

Wyckoff Sets of Space Group P42mc (No. 105)

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

Letter Mult SS Rep. Equivalent WP
f 8 1 (x, y, z) f
e 4 .m. (x, 1/2 , z) de
d 4 .m. (x, 0, z) de
c 2 2mm . (0, 1/2 , z) c
b 2 2mm . (1/2 , 1/2 , z) ab
a 2 2mm . (0, 0, z) ab

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P42mc (105) 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
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 c e d f
3-x,-y,-z
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1    0
)
-1 0,0,0 
a b c d e f
4-x+1/2,-y+1/2,-z
(
  -1   0   0   1/2
   0  -1   0   1/2
   0   0  -1    0
)
-1 1/4,1/4,0 
b a c e d f




Additional traslations generators


No. # Continuous TranslationsGeometrical Interpretation Transformed WP
1 x,y,z+t
(
   1   0   0    0
   0   1   0    0
   0   0   1    t
)
t (0,0,t) 
a b c d e f


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