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

Wyckoff Sets of Space Group P-3 (No. 147)

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

Letter Mult SS Rep. Equivalent WP
g 6 1 (x, y, z) g
f 3 -1 (1/2 , 0, 1/2 ) ef
e 3 -1 (1/2 , 0, 0) ef
d 2 3.. (1/3 , 2/3 , z) d
c 2 3.. (0, 0, z) c
b 1 -3.. (0, 0, 1/2 ) ab
a 1 -3.. (0, 0, 0) ab

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P-3 (147) under the coset representatives of its affine normalizer


The affine normalizer coincides with the Euclidean one.

Index: 8

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
2x,y,z+1/2
(
   1   0   0    0
   0   1   0    0
   0   0   1   1/2
)
t (0,0,1/2) 
b a c d f e g
3-x,-y,z
(
  -1   0   0    0
   0  -1   0    0
   0   0   1    0
)
2 0,0,z 
a b c d e f g
4-x,-y,z+1/2
(
  -1   0   0    0
   0  -1   0    0
   0   0   1   1/2
)
2 (0,0,1/2) 0,0,z 
b a c d f e g
5y,x,z
(
   0   1   0    0
   1   0   0    0
   0   0   1    0
)
m x,x,z 
a b c d e f g
6y,x,z+1/2
(
   0   1   0    0
   1   0   0    0
   0   0   1   1/2
)
c x,x,z 
b a c d f e g
7-y,-x,z
(
   0  -1   0    0
  -1   0   0    0
   0   0   1    0
)
m x,-x,z 
a b c d e f g
8-y,-x,z+1/2
(
   0  -1   0    0
  -1   0   0    0
   0   0   1   1/2
)
c x,-x,z 
b a c d f e g


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