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

Wyckoff Sets of Space Group Fmmm (No. 69)

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
p 32 1 (x, y, z) p p
o 16 ..m (x, y, 0) o mno
n 16 .m. (x, 0, z) n mno
m 16 m.. (0, y, z) m mno
l 16 2.. (x, 1/4 , 1/4 ) l jkl
k 16 .2. (1/4 , y, 1/4 ) k jkl
j 16 ..2 (1/4 , 1/4 , z) j jkl
i 8 mm2 (0, 0, z) i ghi
h 8 m2m (0, y, 0) h ghi
g 8 2mm (x, 0, 0) g ghi
f 8 222 (1/4 , 1/4 , 1/4 ) f f
e 8 ..2/m (1/4 , 1/4 , 0) e cde
d 8 .2/m. (1/4 , 0, 1/4 ) d cde
c 8 2/m.. (0, 1/4 , 1/4 ) c cde
b 4 mmm (0, 0, 1/2 ) ab ab
a 4 mmm (0, 0, 0) ab ab

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of Fmmm (069) under the coset representatives of its affine normalizer


Index: 12

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 g h i j k l m n o p
2z,x,y
(
   0   0   1    0
   1   0   0    0
   0   1   0    0
)
 
a b e c d f i g h k l j o m n p
3y,z,x
(
   0   1   0    0
   0   0   1    0
   1   0   0    0
)
 
a b d e c f h i g l j k n o m p
4y,x,z
(
   0   1   0    0
   1   0   0    0
   0   0   1    0
)
 
a b d c e f h g i j l k n m o p
5z,y,x
(
   0   0   1    0
   0   1   0    0
   1   0   0    0
)
 
a b e d c f i h g l k j o n m p
6x,z,y
(
   1   0   0    0
   0   0   1    0
   0   1   0    0
)
 
a b c e d f g i h k j l m o n p
7x+1/2,y,z
(
   1   0   0   1/2
   0   1   0    0
   0   0   1    0
)
 
b a c d e f g h i j k l m n o p
8z+1/2,x,y
(
   0   0   1   1/2
   1   0   0    0
   0   1   0    0
)
 
b a e c d f i g h k l j o m n p
9y+1/2,z,x
(
   0   1   0   1/2
   0   0   1    0
   1   0   0    0
)
 
b a d e c f h i g l j k n o m p
10y+1/2,x,z
(
   0   1   0   1/2
   1   0   0    0
   0   0   1    0
)
 
b a d c e f h g i j l k n m o p
11z+1/2,y,x
(
   0   0   1   1/2
   0   1   0    0
   1   0   0    0
)
 
b a e d c f i h g l k j o n m p
12x+1/2,z,y
(
   1   0   0   1/2
   0   0   1    0
   0   1   0    0
)
 
b a c e d f g i h k j l m o n p


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