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

Wyckoff Sets of Space Group P63/m (No. 176)

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

Letter Mult SS Rep. Equivalent WP
i 12 1 (x, y, z) i
h 6 m.. (x, y, 1/4 ) h
g 6 -1 (1/2 , 0, 0) g
f 4 3.. (1/3 , 2/3 , z) f
e 4 3.. (0, 0, z) e
d 2 -6.. (2/3 , 1/3 , 1/4 ) cd
c 2 -6.. (1/3 , 2/3 , 1/4 ) cd
b 2 -3.. (0, 0, 0) b
a 2 -6.. (0, 0, 1/4 ) a

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P63/m (176) 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
2x,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
3y,x,z
(
   0   1   0    0
   1   0   0    0
   0   0   1    0
)
m x,x,z 
a b d c e f g h i
4y,x,z+1/2
(
   0   1   0    0
   1   0   0    0
   0   0   1   1/2
)
c x,x,z 
a b c d e f g h i


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