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

Wyckoff Sets of Space Group Ibca (No. 73)

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

Letter Mult SS Rep. Equivalent WP under
Euclidean normalizer
Equivalent WP under
affine normalizer
f 16 1 (x, y, z) f f
e 8 ..2 (0, 1/4 , z) e cde
d 8 .2. (1/4 , y, 0) d cde
c 8 2.. (x, 0, 1/4 ) c cde
b 8 -1 (1/4 , 1/4 , 1/4 ) b ab
a 8 -1 (0, 0, 0) a ab

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Transformation of the Wyckoff Positions of Ibca (073) under the coset representatives of its affine normalizer


Index: 24

No. # Coset Representative Transformed WP
1x,y,z
(
   1   0   0    0
   0   1   0    0
   0   0   1    0
)
a b c d e f
2z,x,y
(
   0   0   1    0
   1   0   0    0
   0   1   0    0
)
a b e c d f
3y,z,x
(
   0   1   0    0
   0   0   1    0
   1   0   0    0
)
a b d e c f
4y+1/4,x+1/4,z+1/4
(
   0   1   0   1/4
   1   0   0   1/4
   0   0   1   1/4
)
b a d c e f
5z+1/4,y+1/4,x+1/4
(
   0   0   1   1/4
   0   1   0   1/4
   1   0   0   1/4
)
b a e d c f
6x+1/4,z+1/4,y+1/4
(
   1   0   0   1/4
   0   0   1   1/4
   0   1   0   1/4
)
b a c e d f
7x+1/2,y,z
(
   1   0   0   1/2
   0   1   0    0
   0   0   1    0
)
a b c d e f
8z+1/2,x,y
(
   0   0   1   1/2
   1   0   0    0
   0   1   0    0
)
a b e c d f
9y+1/2,z,x
(
   0   1   0   1/2
   0   0   1    0
   1   0   0    0
)
a b d e c f
10y+3/4,x+1/4,z+1/4
(
   0   1   0   3/4
   1   0   0   1/4
   0   0   1   1/4
)
b a d c e f
11z+3/4,y+1/4,x+1/4
(
   0   0   1   3/4
   0   1   0   1/4
   1   0   0   1/4
)
b a e d c f
12x+3/4,z+1/4,y+1/4
(
   1   0   0   3/4
   0   0   1   1/4
   0   1   0   1/4
)
b a c e d f
13x,y+1/2,z
(
   1   0   0    0
   0   1   0   1/2
   0   0   1    0
)
a b c d e f
14z,x+1/2,y
(
   0   0   1    0
   1   0   0   1/2
   0   1   0    0
)
a b e c d f
15y,z+1/2,x
(
   0   1   0    0
   0   0   1   1/2
   1   0   0    0
)
a b d e c f
16y+1/4,x+3/4,z+1/4
(
   0   1   0   1/4
   1   0   0   3/4
   0   0   1   1/4
)
b a d c e f
17z+1/4,y+3/4,x+1/4
(
   0   0   1   1/4
   0   1   0   3/4
   1   0   0   1/4
)
b a e d c f
18x+1/4,z+3/4,y+1/4
(
   1   0   0   1/4
   0   0   1   3/4
   0   1   0   1/4
)
b a c e d f
19x+1/2,y+1/2,z
(
   1   0   0   1/2
   0   1   0   1/2
   0   0   1    0
)
a b c d e f
20z+1/2,x+1/2,y
(
   0   0   1   1/2
   1   0   0   1/2
   0   1   0    0
)
a b e c d f
21y+1/2,z+1/2,x
(
   0   1   0   1/2
   0   0   1   1/2
   1   0   0    0
)
a b d e c f
22y+3/4,x+3/4,z+1/4
(
   0   1   0   3/4
   1   0   0   3/4
   0   0   1   1/4
)
b a d c e f
23z+3/4,y+3/4,x+1/4
(
   0   0   1   3/4
   0   1   0   3/4
   1   0   0   1/4
)
b a e d c f
24x+3/4,z+3/4,y+1/4
(
   1   0   0   3/4
   0   0   1   3/4
   0   1   0   1/4
)
b a c e d f


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