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

Wyckoff Sets of Space Group P-1 (No. 2)

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

Letter Mult SS Rep. Equivalent WP
i 2 1 (x, y, z) i
h 1 -1 (1/2 , 1/2 , 1/2 ) abcdefgh
g 1 -1 (0, 1/2 , 1/2 ) abcdefgh
f 1 -1 (1/2 , 0, 1/2 ) abcdefgh
e 1 -1 (1/2 , 1/2 , 0) abcdefgh
d 1 -1 (1/2 , 0, 0) abcdefgh
c 1 -1 (0, 1/2 , 0) abcdefgh
b 1 -1 (0, 0, 1/2 ) abcdefgh
a 1 -1 (0, 0, 0) abcdefgh

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P-1 (002) under the coset representatives of its Euclidean normalizer


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


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