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

Wyckoff Sets of Space Group P-4m2 (No. 115)

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

Letter Mult SS Rep. Equivalent WP
l 8 1 (x, y, z) l
k 4 .m. (x, 1/2 , z) jk
j 4 .m. (x, 0, z) jk
i 4 ..2 (x, x, 1/2 ) hi
h 4 ..2 (x, x, 0) hi
g 2 2mm . (0, 1/2 , z) g
f 2 2mm . (1/2 , 1/2 , z) ef
e 2 2mm . (0, 0, z) ef
d 1 -4m2 (0, 0, 1/2 ) abcd
c 1 -4m2 (1/2 , 1/2 , 1/2 ) abcd
b 1 -4m2 (1/2 , 1/2 , 0) abcd
a 1 -4m2 (0, 0, 0) abcd

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P-4m2 (115) 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 h i j k l
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)
b a d c f e g h i k j l
3x,y,z+1/2
(
   1   0   0    0
   0   1   0    0
   0   0   1   1/2
)
t (0,0,1/2)
d c b a e f g i h j k l
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)
c d a b f e g i h k j l
5-x,-y,-z
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1    0
)
-1 0,0,0
a b c d e f g h i j k l
6-x+1/2,-y+1/2,-z
(
  -1   0   0   1/2
   0  -1   0   1/2
   0   0  -1    0
)
-1 1/4,1/4,0
b a d c f e g h i k j l
7-x,-y,-z+1/2
(
  -1   0   0    0
   0  -1   0    0
   0   0  -1   1/2
)
-1 0,0,1/4
d c b a e f g i h j k l
8-x+1/2,-y+1/2,-z+1/2
(
  -1   0   0   1/2
   0  -1   0   1/2
   0   0  -1   1/2
)
-1 1/4,1/4,1/4
c d a b f e g i h k j l


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