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

Wyckoff Sets of Space Group P4/mmm (No. 123)

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

Letter Mult SS Rep. Equivalent WP
u 16 1 (x, y, z) u
t 8 .m. (x, 1/2 , z) st
s 8 .m. (x, 0, z) st
r 8 ..m (x, x, z) r
q 8 m.. (x, y, 1/2 ) pq
p 8 m.. (x, y, 0) pq
o 4 m2m . (x, 1/2 , 1/2 ) lmno
n 4 m2m . (x, 1/2 , 0) lmno
m 4 m2m . (x, 0, 1/2 ) lmno
l 4 m2m . (x, 0, 0) lmno
k 4 m.2 m (x, x, 1/2 ) jk
j 4 m.2 m (x, x, 0) jk
i 4 2mm . (0, 1/2 , z) i
h 2 4mm (1/2 , 1/2 , z) gh
g 2 4mm (0, 0, z) gh
f 2 mmm . (0, 1/2 , 0) ef
e 2 mmm . (0, 1/2 , 1/2 ) ef
d 1 4/mmm (1/2 , 1/2 , 1/2 ) abcd
c 1 4/mmm (1/2 , 1/2 , 0) abcd
b 1 4/mmm (0, 0, 1/2 ) abcd
a 1 4/mmm (0, 0, 0) abcd

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P4/mmm (123) 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 j k l m n o p q r s t u
2x+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) 
c d a b e f h g i j k n o l m p q r t s u
3x,y,z+1/2
(
   1   0   0    0
   0   1   0    0
   0   0   1   1/2
)
t (0,0,1/2) 
b a d c f e g h i k j m l o n q p r s t u
4x+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) 
d c b a f e h g i k j o n m l q p r t s u


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