[Index of services] [New input] 
Result of symbol lookup:
  Space group number: 228
  Schoenflies symbol: Oh^8
  Hermann-Mauguin symbol: F d -3 c
  Origin choice: 2
  Hall symbol: -F 4ud 2vw 3

Input space group symbol: F d -3 c :2
Convention: Default

Number of lattice translations: 4
Space group is centric.
Number of representative symmetry operations: 24
Total number of symmetry operations: 192

Parallelepiped containing an asymmetric unit:
  0<=x<=1/8; 0<=y<=1/8; 0<=z<1/2

List of symmetry operations:
Matrix Rotation-part type Axis direction Screw/glide component Origin shift
x,y,z 1---
-y+1/2,x+1/4,z+1/4 4^1[0,0,1]0,0,1/41/8,3/8,0
-x+1/4,-y+3/4,z+1/2 2[0,0,1]0,0,1/21/8,3/8,0
y+3/4,-x+1/2,z+3/4 4^-1[0,0,1]0,0,3/45/8,-1/8,0
x,-y+1/4,-z+1/4 2[1,0,0]0,0,00,1/8,1/8
y+1/4,x+1/4,-z+1/2 2[1,1,0]1/4,1/4,00,0,1/4
-x+1/4,y+1/2,-z+3/4 2[0,1,0]0,1/2,01/8,0,3/8
-y,-x+1/2,-z 2[-1,1,0]-1/4,1/4,01/4,0,0
z,x,y 3^1[1,1,1]0,0,00,0,0
-x+1/2,z+1/4,y+1/4 2[0,1,1]0,1/4,1/41/4,0,0
-z+1/4,-x+3/4,y+1/2 3^-1[-1,1,1]-1/3,1/3,1/37/12,-1/6,0
x+3/4,-z+1/2,y+3/4 4^1[1,0,0]3/4,0,00,-1/8,5/8
z,-x+1/4,-y+1/4 3^-1[1,-1,1]0,0,00,1/4,0
x+1/4,z+1/4,-y+1/2 4^-1[1,0,0]1/4,0,00,3/8,1/8
-z+1/4,x+1/2,-y+3/4 3^1[-1,-1,1]0,0,01/4,3/4,0
-x,-z+1/2,-y 2[0,-1,1]0,1/4,-1/40,1/4,0
y,z,x 3^-1[1,1,1]0,0,00,0,0
y+1/2,-z+1/4,-x+3/4 3^-1[-1,-1,1]0,0,03/4,1/4,0
z+1/4,y+3/4,-x 4^1[0,1,0]0,3/4,01/8,0,-1/8
-y+3/4,z+1/2,-x+1/4 3^1[-1,1,1]0,0,01/4,1/2,0
-z+1/2,-y+1/2,-x+1/2 2[-1,0,1]0,0,01/2,1/4,0
-y+1/4,-z+1/4,x 3^1[1,-1,1]0,0,00,1/4,0
z+1/4,-y,x+3/4 2[1,0,1]1/2,0,1/2-1/4,0,0
-z,y+3/4,x+1/4 4^-1[0,1,0]0,3/4,0-1/8,0,1/8
-x,-y,-z -1--0,0,0
y-1/2,-x-1/4,-z-1/4 -4^1[0,0,1]0,0,0-3/8,1/8,-1/8
x-1/4,y-3/4,-z-1/2 -2[0,0,1]-1/4,-3/4,00,0,-1/4
-y-3/4,x-1/2,-z-3/4 -4^-1[0,0,1]0,0,0-1/8,-5/8,-3/8
-x,y-1/4,z-1/4 -2[1,0,0]0,-1/4,-1/40,0,0
-y-1/4,-x-1/4,z-1/2 -2[1,1,0]0,0,-1/2-1/4,0,0
x-1/4,-y-1/2,z-3/4 -2[0,1,0]-1/4,0,-3/40,-1/4,0
y,x-1/2,z -2[-1,1,0]-1/4,-1/4,01/4,0,0
-z,-x,-y -3^1[1,1,1]0,0,00,0,0
x-1/2,-z-1/4,-y-1/4 -2[0,1,1]-1/2,0,00,-1/4,0
z-1/4,x-3/4,-y-1/2 -3^-1[-1,1,1]0,0,00,-3/4,1/4
-x-3/4,z-1/2,-y-3/4 -4^1[1,0,0]0,0,0-3/8,-5/8,-1/8
-z,x-1/4,y-1/4 -3^-1[1,-1,1]0,0,01/4,0,-1/4
-x-1/4,-z-1/4,y-1/2 -4^-1[1,0,0]0,0,0-1/8,1/8,-3/8
z-1/4,-x-1/2,y-3/4 -3^1[-1,-1,1]0,0,0-3/4,1/4,-1/2
x,z-1/2,y -2[0,-1,1]0,-1/4,-1/40,-1/4,0
-y,-z,-x -3^-1[1,1,1]0,0,00,0,0
-y-1/2,z-1/4,x-3/4 -3^-1[-1,-1,1]0,0,01/4,-3/4,-1/2
-z-1/4,-y-3/4,x -4^1[0,1,0]0,0,0-1/8,-3/8,-1/8
y-3/4,-z-1/2,x-1/4 -3^1[-1,1,1]0,0,0-1/2,1/4,-3/4
z-1/2,y-1/2,x-1/2 -2[-1,0,1]-1/2,-1/2,-1/20,0,0
y-1/4,z-1/4,-x -3^1[1,-1,1]0,0,0-1/4,0,1/4
-z-1/4,y,-x-3/4 -2[1,0,1]1/4,0,-1/4-1/2,0,0
z,-y-3/4,-x-1/4 -4^-1[0,1,0]0,0,0-1/8,-3/8,-1/8
x,y+1/2,z+1/2 1---
-y+1/2,x+3/4,z+3/4 4^1[0,0,1]0,0,3/4-1/8,5/8,0
-x+1/4,-y+5/4,z+1 2[0,0,1]0,0,11/8,5/8,0
y+3/4,-x+1,z+5/4 4^-1[0,0,1]0,0,5/47/8,1/8,0
x,-y+3/4,-z+3/4 2[1,0,0]0,0,00,3/8,3/8
y+1/4,x+3/4,-z+1 2[1,1,0]1/2,1/2,0-1/4,0,1/2
-x+1/4,y+1,-z+5/4 2[0,1,0]0,1,01/8,0,5/8
-y,-x+1,-z+1/2 2[-1,1,0]-1/2,1/2,01/2,0,1/4
z,x+1/2,y+1/2 3^1[1,1,1]1/3,1/3,1/3-1/3,-1/6,0
-x+1/2,z+3/4,y+3/4 2[0,1,1]0,3/4,3/41/4,0,0
-z+1/4,-x+5/4,y+1 3^-1[-1,1,1]-2/3,2/3,2/311/12,-1/3,0
x+3/4,-z+1,y+5/4 4^1[1,0,0]3/4,0,00,-1/8,9/8
z,-x+3/4,-y+3/4 3^-1[1,-1,1]0,0,00,3/4,0
x+1/4,z+3/4,-y+1 4^-1[1,0,0]1/4,0,00,7/8,1/8
-z+1/4,x+1,-y+5/4 3^1[-1,-1,1]0,0,01/4,5/4,0
-x,-z+1,-y+1/2 2[0,-1,1]0,1/4,-1/40,3/4,0
y,z+1/2,x+1/2 3^-1[1,1,1]1/3,1/3,1/3-1/6,1/6,0
y+1/2,-z+3/4,-x+5/4 3^-1[-1,-1,1]0,0,05/4,3/4,0
z+1/4,y+5/4,-x+1/2 4^1[0,1,0]0,5/4,03/8,0,1/8
-y+3/4,z+1,-x+3/4 3^1[-1,1,1]-1/3,1/3,1/35/12,2/3,0
-z+1/2,-y+1,-x+1 2[-1,0,1]-1/4,0,1/43/4,1/2,0
-y+1/4,-z+3/4,x+1/2 3^1[1,-1,1]0,0,0-1/2,3/4,0
z+1/4,-y+1/2,x+5/4 2[1,0,1]3/4,0,3/4-1/2,1/4,0
-z,y+5/4,x+3/4 4^-1[0,1,0]0,5/4,0-3/8,0,3/8
-x,-y+1/2,-z+1/2 -1--0,1/4,1/4
y-1/2,-x+1/4,-z+1/4 -4^1[0,0,1]0,0,0-1/8,3/8,1/8
x-1/4,y-1/4,-z -2[0,0,1]-1/4,-1/4,00,0,0
-y-3/4,x,-z-1/4 -4^-1[0,0,1]0,0,0-3/8,-3/8,-1/8
-x,y+1/4,z+1/4 -2[1,0,0]0,1/4,1/40,0,0
-y-1/4,-x+1/4,z -2[1,1,0]-1/4,1/4,00,0,0
x-1/4,-y,z-1/4 -2[0,1,0]-1/4,0,-1/40,0,0
y,x,z+1/2 -2[-1,1,0]0,0,1/20,0,0
-z,-x+1/2,-y+1/2 -3^1[1,1,1]0,0,00,1/2,0
x-1/2,-z+1/4,-y+1/4 -2[0,1,1]-1/2,0,00,1/4,0
z-1/4,x-1/4,-y -3^-1[-1,1,1]0,0,00,-1/4,1/4
-x-3/4,z,-y-1/4 -4^1[1,0,0]0,0,0-3/8,-1/8,-1/8
-z,x+1/4,y+1/4 -3^-1[1,-1,1]0,0,0-1/4,0,1/4
-x-1/4,-z+1/4,y -4^-1[1,0,0]0,0,0-1/8,1/8,1/8
z-1/4,-x,y-1/4 -3^1[-1,-1,1]0,0,0-1/4,1/4,0
x,z,y+1/2 -2[0,-1,1]0,1/4,1/40,-1/4,0
-y,-z+1/2,-x+1/2 -3^-1[1,1,1]0,0,00,0,1/2
-y-1/2,z+1/4,x-1/4 -3^-1[-1,-1,1]0,0,0-1/4,-1/4,-1/2
-z-1/4,-y-1/4,x+1/2 -4^1[0,1,0]0,0,0-3/8,-1/8,1/8
y-3/4,-z,x+1/4 -3^1[-1,1,1]0,0,0-1/2,1/4,-1/4
z-1/2,y,x -2[-1,0,1]-1/4,0,-1/4-1/4,0,0
y-1/4,z+1/4,-x+1/2 -3^1[1,-1,1]0,0,01/4,1/2,1/4
-z-1/4,y+1/2,-x-1/4 -2[1,0,1]0,1/2,0-1/4,0,0
z,-y-1/4,-x+1/4 -4^-1[0,1,0]0,0,01/8,-1/8,1/8
x+1/2,y,z+1/2 1---
-y+1,x+1/4,z+3/4 4^1[0,0,1]0,0,3/43/8,5/8,0
-x+3/4,-y+3/4,z+1 2[0,0,1]0,0,13/8,3/8,0
y+5/4,-x+1/2,z+5/4 4^-1[0,0,1]0,0,5/47/8,-3/8,0
x+1/2,-y+1/4,-z+3/4 2[1,0,0]1/2,0,00,1/8,3/8
y+3/4,x+1/4,-z+1 2[1,1,0]1/2,1/2,01/4,0,1/2
-x+3/4,y+1/2,-z+5/4 2[0,1,0]0,1/2,03/8,0,5/8
-y+1/2,-x+1/2,-z+1/2 2[-1,1,0]0,0,01/2,0,1/4
z+1/2,x,y+1/2 3^1[1,1,1]1/3,1/3,1/31/6,-1/6,0
-x+1,z+1/4,y+3/4 2[0,1,1]0,1/2,1/21/2,-1/4,0
-z+3/4,-x+3/4,y+1 3^-1[-1,1,1]-1/3,1/3,1/313/12,-2/3,0
x+5/4,-z+1/2,y+5/4 4^1[1,0,0]5/4,0,00,-3/8,7/8
z+1/2,-x+1/4,-y+3/4 3^-1[1,-1,1]1/3,-1/3,1/31/6,5/12,0
x+3/4,z+1/4,-y+1 4^-1[1,0,0]3/4,0,00,5/8,3/8
-z+3/4,x+1/2,-y+5/4 3^1[-1,-1,1]0,0,03/4,5/4,0
-x+1/2,-z+1/2,-y+1/2 2[0,-1,1]0,0,01/4,1/2,0
y+1/2,z,x+1/2 3^-1[1,1,1]1/3,1/3,1/3-1/6,-1/3,0
y+1,-z+1/4,-x+5/4 3^-1[-1,-1,1]0,0,05/4,1/4,0
z+3/4,y+3/4,-x+1/2 4^1[0,1,0]0,3/4,05/8,0,-1/8
-y+5/4,z+1/2,-x+3/4 3^1[-1,1,1]0,0,03/4,1/2,0
-z+1,-y+1/2,-x+1 2[-1,0,1]0,0,01,1/4,0
-y+3/4,-z+1/4,x+1/2 3^1[1,-1,1]1/3,-1/3,1/3-1/6,7/12,0
z+3/4,-y,x+5/4 2[1,0,1]1,0,1-1/4,0,0
-z+1/2,y+3/4,x+3/4 4^-1[0,1,0]0,3/4,0-1/8,0,5/8
-x+1/2,-y,-z+1/2 -1--1/4,0,1/4
y,-x-1/4,-z+1/4 -4^1[0,0,1]0,0,0-1/8,-1/8,1/8
x+1/4,y-3/4,-z -2[0,0,1]1/4,-3/4,00,0,0
-y-1/4,x-1/2,-z-1/4 -4^-1[0,0,1]0,0,01/8,-3/8,-1/8
-x+1/2,y-1/4,z+1/4 -2[1,0,0]0,-1/4,1/41/4,0,0
-y+1/4,-x-1/4,z -2[1,1,0]1/4,-1/4,00,0,0
x+1/4,-y-1/2,z-1/4 -2[0,1,0]1/4,0,-1/40,-1/4,0
y+1/2,x-1/2,z+1/2 -2[-1,1,0]0,0,1/21/2,0,0
-z+1/2,-x,-y+1/2 -3^1[1,1,1]0,0,00,0,1/2
x,-z-1/4,-y+1/4 -2[0,1,1]0,-1/4,1/40,0,0
z+1/4,x-3/4,-y -3^-1[-1,1,1]0,0,01/2,-1/4,1/4
-x-1/4,z-1/2,-y-1/4 -4^1[1,0,0]0,0,0-1/8,-3/8,1/8
-z+1/2,x-1/4,y+1/4 -3^-1[1,-1,1]0,0,01/4,0,1/4
-x+1/4,-z-1/4,y -4^-1[1,0,0]0,0,01/8,-1/8,-1/8
z+1/4,-x-1/2,y-1/4 -3^1[-1,-1,1]0,0,0-1/4,-1/4,-1/2
x+1/2,z-1/2,y+1/2 -2[0,-1,1]1/2,0,00,-1/2,0
-y+1/2,-z,-x+1/2 -3^-1[1,1,1]0,0,01/2,0,0
-y,z-1/4,x-1/4 -3^-1[-1,-1,1]0,0,01/4,-1/4,0
-z+1/4,-y-3/4,x+1/2 -4^1[0,1,0]0,0,0-1/8,-3/8,3/8
y-1/4,-z-1/2,x+1/4 -3^1[-1,1,1]0,0,0-1/2,-1/4,-1/4
z,y-1/2,x -2[-1,0,1]0,-1/2,00,0,0
y+1/4,z-1/4,-x+1/2 -3^1[1,-1,1]0,0,01/4,0,1/4
-z+1/4,y,-x-1/4 -2[1,0,1]1/4,0,-1/40,0,0
z+1/2,-y-3/4,-x+1/4 -4^-1[0,1,0]0,0,03/8,-3/8,-1/8
x+1/2,y+1/2,z 1---
-y+1,x+3/4,z+1/4 4^1[0,0,1]0,0,1/41/8,7/8,0
-x+3/4,-y+5/4,z+1/2 2[0,0,1]0,0,1/23/8,5/8,0
y+5/4,-x+1,z+3/4 4^-1[0,0,1]0,0,3/49/8,-1/8,0
x+1/2,-y+3/4,-z+1/4 2[1,0,0]1/2,0,00,3/8,1/8
y+3/4,x+3/4,-z+1/2 2[1,1,0]3/4,3/4,00,0,1/4
-x+3/4,y+1,-z+3/4 2[0,1,0]0,1,03/8,0,3/8
-y+1/2,-x+1,-z 2[-1,1,0]-1/4,1/4,03/4,0,0
z+1/2,x+1/2,y 3^1[1,1,1]1/3,1/3,1/31/6,1/3,0
-x+1,z+3/4,y+1/4 2[0,1,1]0,1/2,1/21/2,1/4,0
-z+3/4,-x+5/4,y+1/2 3^-1[-1,1,1]-1/3,1/3,1/313/12,-1/6,0
x+5/4,-z+1,y+3/4 4^1[1,0,0]5/4,0,00,1/8,7/8
z+1/2,-x+3/4,-y+1/4 3^-1[1,-1,1]0,0,01/2,1/4,0
x+3/4,z+3/4,-y+1/2 4^-1[1,0,0]3/4,0,00,5/8,-1/8
-z+3/4,x+1,-y+3/4 3^1[-1,-1,1]1/3,1/3,-1/35/12,13/12,0
-x+1/2,-z+1,-y 2[0,-1,1]0,1/2,-1/21/4,1/2,0
y+1/2,z+1/2,x 3^-1[1,1,1]1/3,1/3,1/31/3,1/6,0
y+1,-z+3/4,-x+3/4 3^-1[-1,-1,1]1/3,1/3,-1/313/12,5/12,0
z+3/4,y+5/4,-x 4^1[0,1,0]0,5/4,03/8,0,-3/8
-y+5/4,z+1,-x+1/4 3^1[-1,1,1]0,0,01/4,1,0
-z+1,-y+1,-x+1/2 2[-1,0,1]1/4,0,-1/43/4,1/2,0
-y+3/4,-z+3/4,x 3^1[1,-1,1]0,0,00,3/4,0
z+3/4,-y+1/2,x+3/4 2[1,0,1]3/4,0,3/40,1/4,0
-z+1/2,y+5/4,x+1/4 4^-1[0,1,0]0,5/4,01/8,0,3/8
-x+1/2,-y+1/2,-z -1--1/4,1/4,0
y,-x+1/4,-z-1/4 -4^1[0,0,1]0,0,01/8,1/8,-1/8
x+1/4,y-1/4,-z-1/2 -2[0,0,1]1/4,-1/4,00,0,-1/4
-y-1/4,x,-z-3/4 -4^-1[0,0,1]0,0,0-1/8,-1/8,-3/8
-x+1/2,y+1/4,z-1/4 -2[1,0,0]0,1/4,-1/41/4,0,0
-y+1/4,-x+1/4,z-1/2 -2[1,1,0]0,0,-1/21/4,0,0
x+1/4,-y,z-3/4 -2[0,1,0]1/4,0,-3/40,0,0
y+1/2,x,z -2[-1,1,0]1/4,1/4,01/4,0,0
-z+1/2,-x+1/2,-y -3^1[1,1,1]0,0,01/2,0,0
x,-z+1/4,-y-1/4 -2[0,1,1]0,1/4,-1/40,0,0
z+1/4,x-1/4,-y-1/2 -3^-1[-1,1,1]0,0,00,-1/4,-1/4
-x-1/4,z,-y-3/4 -4^1[1,0,0]0,0,0-1/8,-3/8,-3/8
-z+1/2,x+1/4,y-1/4 -3^-1[1,-1,1]0,0,01/4,1/2,1/4
-x+1/4,-z+1/4,y-1/2 -4^-1[1,0,0]0,0,01/8,3/8,-1/8
z+1/4,-x,y-3/4 -3^1[-1,-1,1]0,0,0-1/4,1/4,-1/2
x+1/2,z,y -2[0,-1,1]1/2,0,00,0,0
-y+1/2,-z+1/2,-x -3^-1[1,1,1]0,0,00,1/2,0
-y,z+1/4,x-3/4 -3^-1[-1,-1,1]0,0,01/4,-1/4,-1/2
-z+1/4,-y-1/4,x -4^1[0,1,0]0,0,01/8,-1/8,1/8
y-1/4,-z,x-1/4 -3^1[-1,1,1]0,0,00,1/4,-1/4
z,y,x-1/2 -2[-1,0,1]-1/4,0,-1/41/4,0,0
y+1/4,z+1/4,-x -3^1[1,-1,1]0,0,01/4,0,-1/4
-z+1/4,y+1/2,-x-3/4 -2[1,0,1]1/2,1/2,-1/2-1/4,0,0
z+1/2,-y-1/4,-x-1/4 -4^-1[0,1,0]0,0,01/8,-1/8,-3/8 

List of Wyckoff positions:
Wyckoff letter Multiplicity Site symmetry
point group type 		Representative special position operator
h1921x,y,z
g9621/4,y,-y
f962x,1/8,1/8
e643x,x,x
d48-4-1/8,1/8,1/8
c32-30,0,0
b32321/4,1/4,1/4
a16231/8,1/8,1/8 

Harker planes:
Algebraic Normal vector A point in the plane
x-y+1/2,-x-y+1/4,1/4[0,0,1]1/2,1/4,1/4
2*x+1/4,2*y+3/4,1/2[0,0,1]1/4,3/4,1/2
0,2*y+1/4,2*z+1/4[1,0,0]0,1/4,1/4
x+y+1/4,-x-y+1/4,2*z+1/2[1,1,0]1/4,1/4,1/2
2*x+1/4,1/2,2*z+3/4[0,1,0]1/4,1/2,3/4
x+y,x+y+1/2,2*z[-1,1,0]0,1/2,0
x+z,-x-y,y-z[1,1,1]0,0,0
2*x+1/2,y+z+1/4,-y-z+1/4[0,1,1]1/2,1/4,1/4
3/4,y-z+1/2,-y-z+3/4[1,0,0]3/4,1/2,3/4
x+z+1/4,-x-y+1/2,-y+z+3/4[-1,-1,1]1/4,1/2,3/4
2*x,y+z+1/2,y+z[0,-1,1]0,1/2,0
x-z+1/4,3/4,x+z[0,1,0]1/4,3/4,0
x+y+3/4,y-z+1/2,x+z+1/4[-1,1,1]3/4,1/2,1/4
x+z+1/2,2*y+1/2,x+z+1/2[-1,0,1]1/2,1/2,1/2
x+y+1/4,y-z+1/4,-x-z[1,-1,1]1/4,1/4,0
x+z+1/4,2*y,-x-z+3/4[1,0,1]1/4,0,3/4 

Additional generators of Euclidean normalizer:
  Number of structure-seminvariant vectors and moduli: 1
    Vector    Modulus
    (1, 0, 0) 2

Grid factors implied by symmetries:
  Space group: (4, 4, 4)
  Structure-seminvariant vectors and moduli: (2, 1, 1)
  Euclidean normalizer: (4, 4, 4)

  All points of a grid over the unit cell are mapped
  exactly onto other grid points only if the factors
  shown above are factors of the grid.
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