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

Wyckoff Sets of Space Group P4/mcc (No. 124)

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

Letter Mult SS Rep. Equivalent WP
n 16 1 (x, y, z) n
m 8 m.. (x, y, 0) m
l 8 .2. (x, 1/2 , 1/4 ) kl
k 8 .2. (x, 0, 1/4 ) kl
j 8 ..2 (x, x, 1/4 ) j
i 8 2.. (0, 1/2 , z) i
h 4 4.. (1/2 , 1/2 , z) gh
g 4 4.. (0, 0, z) gh
f 4 222 . (0, 1/2 , 1/4 ) f
e 4 2/m.. (0, 1/2 , 0) e
d 2 4/m.. (1/2 , 1/2 , 0) bd
c 2 422 (1/2 , 1/2 , 1/4 ) ac
b 2 4/m.. (0, 0, 0) bd
a 2 422 (0, 0, 1/4 ) ac

[ Show Wyckoff Positions ]


Transformation of the Wyckoff Positions of P4/mcc (124) 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
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 l k m n
3x,y,z+1/2
(
   1   0   0    0
   0   1   0    0
   0   0   1   1/2
)
t (0,0,1/2)
a b c d e f g h i j k l m n
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 e f h g i j l k m n


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