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<hr>
<pre>
Result of symbol lookup:
  Space group number: 225
  Schoenflies symbol: Oh^5
  Hermann-Mauguin symbol: F m -3 m
  Hall symbol: -F 4 2 3

Input space group symbol: F m -3 m
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&lt;=x&lt;=1/4; 0&lt;=y&lt;=1/4; 0&lt;=z&lt;=1/2

List of symmetry operations:
</pre><table border=2 cellpadding=2>
<tr>
<th>Matrix
<th>Rotation-part type
<th>Axis direction
<th>Screw/glide component
<th>Origin shift
</tr>
<tr>
<td><tt>x,y,z</tt>
<td>1<td>-<td>-<td>-
</tr>
<tr>
<td><tt>-y,x,z</tt>
<td>4^1<td>[0,0,1]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>-x,-y,z</tt>
<td>2<td>[0,0,1]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>y,-x,z</tt>
<td>4^-1<td>[0,0,1]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>x,-y,-z</tt>
<td>2<td>[1,0,0]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>y,x,-z</tt>
<td>2<td>[1,1,0]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>-x,y,-z</tt>
<td>2<td>[0,1,0]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>-y,-x,-z</tt>
<td>2<td>[-1,1,0]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>z,x,y</tt>
<td>3^1<td>[1,1,1]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>-x,z,y</tt>
<td>2<td>[0,1,1]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>-z,-x,y</tt>
<td>3^-1<td>[-1,1,1]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>x,-z,y</tt>
<td>4^1<td>[1,0,0]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>z,-x,-y</tt>
<td>3^-1<td>[1,-1,1]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>x,z,-y</tt>
<td>4^-1<td>[1,0,0]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>-z,x,-y</tt>
<td>3^1<td>[-1,-1,1]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>-x,-z,-y</tt>
<td>2<td>[0,-1,1]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>y,z,x</tt>
<td>3^-1<td>[1,1,1]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>y,-z,-x</tt>
<td>3^-1<td>[-1,-1,1]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>z,y,-x</tt>
<td>4^1<td>[0,1,0]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>-y,z,-x</tt>
<td>3^1<td>[-1,1,1]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>-z,-y,-x</tt>
<td>2<td>[-1,0,1]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>-y,-z,x</tt>
<td>3^1<td>[1,-1,1]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>z,-y,x</tt>
<td>2<td>[1,0,1]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>-z,y,x</tt>
<td>4^-1<td>[0,1,0]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>-x,-y,-z</tt>
<td>-1<td>-<td>-<td>0,0,0
</tr>
<tr>
<td><tt>y,-x,-z</tt>
<td>-4^1<td>[0,0,1]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>x,y,-z</tt>
<td>-2<td>[0,0,1]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>-y,x,-z</tt>
<td>-4^-1<td>[0,0,1]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>-x,y,z</tt>
<td>-2<td>[1,0,0]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>-y,-x,z</tt>
<td>-2<td>[1,1,0]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>x,-y,z</tt>
<td>-2<td>[0,1,0]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>y,x,z</tt>
<td>-2<td>[-1,1,0]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>-z,-x,-y</tt>
<td>-3^1<td>[1,1,1]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>x,-z,-y</tt>
<td>-2<td>[0,1,1]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>z,x,-y</tt>
<td>-3^-1<td>[-1,1,1]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>-x,z,-y</tt>
<td>-4^1<td>[1,0,0]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>-z,x,y</tt>
<td>-3^-1<td>[1,-1,1]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>-x,-z,y</tt>
<td>-4^-1<td>[1,0,0]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>z,-x,y</tt>
<td>-3^1<td>[-1,-1,1]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>x,z,y</tt>
<td>-2<td>[0,-1,1]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>-y,-z,-x</tt>
<td>-3^-1<td>[1,1,1]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>-y,z,x</tt>
<td>-3^-1<td>[-1,-1,1]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>-z,-y,x</tt>
<td>-4^1<td>[0,1,0]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>y,-z,x</tt>
<td>-3^1<td>[-1,1,1]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>z,y,x</tt>
<td>-2<td>[-1,0,1]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>y,z,-x</tt>
<td>-3^1<td>[1,-1,1]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>-z,y,-x</tt>
<td>-2<td>[1,0,1]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>z,-y,-x</tt>
<td>-4^-1<td>[0,1,0]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>x,y+1/2,z+1/2</tt>
<td>1<td>-<td>-<td>-
</tr>
<tr>
<td><tt>-y,x+1/2,z+1/2</tt>
<td>4^1<td>[0,0,1]<td>0,0,1/2<td>-1/4,1/4,0
</tr>
<tr>
<td><tt>-x,-y+1/2,z+1/2</tt>
<td>2<td>[0,0,1]<td>0,0,1/2<td>0,1/4,0
</tr>
<tr>
<td><tt>y,-x+1/2,z+1/2</tt>
<td>4^-1<td>[0,0,1]<td>0,0,1/2<td>1/4,1/4,0
</tr>
<tr>
<td><tt>x,-y+1/2,-z+1/2</tt>
<td>2<td>[1,0,0]<td>0,0,0<td>0,1/4,1/4
</tr>
<tr>
<td><tt>y,x+1/2,-z+1/2</tt>
<td>2<td>[1,1,0]<td>1/4,1/4,0<td>-1/4,0,1/4
</tr>
<tr>
<td><tt>-x,y+1/2,-z+1/2</tt>
<td>2<td>[0,1,0]<td>0,1/2,0<td>0,0,1/4
</tr>
<tr>
<td><tt>-y,-x+1/2,-z+1/2</tt>
<td>2<td>[-1,1,0]<td>-1/4,1/4,0<td>1/4,0,1/4
</tr>
<tr>
<td><tt>z,x+1/2,y+1/2</tt>
<td>3^1<td>[1,1,1]<td>1/3,1/3,1/3<td>-1/3,-1/6,0
</tr>
<tr>
<td><tt>-x,z+1/2,y+1/2</tt>
<td>2<td>[0,1,1]<td>0,1/2,1/2<td>0,0,0
</tr>
<tr>
<td><tt>-z,-x+1/2,y+1/2</tt>
<td>3^-1<td>[-1,1,1]<td>-1/3,1/3,1/3<td>1/3,-1/6,0
</tr>
<tr>
<td><tt>x,-z+1/2,y+1/2</tt>
<td>4^1<td>[1,0,0]<td>0,0,0<td>0,0,1/2
</tr>
<tr>
<td><tt>z,-x+1/2,-y+1/2</tt>
<td>3^-1<td>[1,-1,1]<td>0,0,0<td>0,1/2,0
</tr>
<tr>
<td><tt>x,z+1/2,-y+1/2</tt>
<td>4^-1<td>[1,0,0]<td>0,0,0<td>0,1/2,0
</tr>
<tr>
<td><tt>-z,x+1/2,-y+1/2</tt>
<td>3^1<td>[-1,-1,1]<td>0,0,0<td>0,1/2,0
</tr>
<tr>
<td><tt>-x,-z+1/2,-y+1/2</tt>
<td>2<td>[0,-1,1]<td>0,0,0<td>0,1/2,0
</tr>
<tr>
<td><tt>y,z+1/2,x+1/2</tt>
<td>3^-1<td>[1,1,1]<td>1/3,1/3,1/3<td>-1/6,1/6,0
</tr>
<tr>
<td><tt>y,-z+1/2,-x+1/2</tt>
<td>3^-1<td>[-1,-1,1]<td>0,0,0<td>1/2,1/2,0
</tr>
<tr>
<td><tt>z,y+1/2,-x+1/2</tt>
<td>4^1<td>[0,1,0]<td>0,1/2,0<td>1/4,0,1/4
</tr>
<tr>
<td><tt>-y,z+1/2,-x+1/2</tt>
<td>3^1<td>[-1,1,1]<td>-1/3,1/3,1/3<td>1/6,1/6,0
</tr>
<tr>
<td><tt>-z,-y+1/2,-x+1/2</tt>
<td>2<td>[-1,0,1]<td>-1/4,0,1/4<td>1/4,1/4,0
</tr>
<tr>
<td><tt>-y,-z+1/2,x+1/2</tt>
<td>3^1<td>[1,-1,1]<td>0,0,0<td>-1/2,1/2,0
</tr>
<tr>
<td><tt>z,-y+1/2,x+1/2</tt>
<td>2<td>[1,0,1]<td>1/4,0,1/4<td>-1/4,1/4,0
</tr>
<tr>
<td><tt>-z,y+1/2,x+1/2</tt>
<td>4^-1<td>[0,1,0]<td>0,1/2,0<td>-1/4,0,1/4
</tr>
<tr>
<td><tt>-x,-y+1/2,-z+1/2</tt>
<td>-1<td>-<td>-<td>0,1/4,1/4
</tr>
<tr>
<td><tt>y,-x+1/2,-z+1/2</tt>
<td>-4^1<td>[0,0,1]<td>0,0,0<td>1/4,1/4,1/4
</tr>
<tr>
<td><tt>x,y+1/2,-z+1/2</tt>
<td>-2<td>[0,0,1]<td>0,1/2,0<td>0,0,1/4
</tr>
<tr>
<td><tt>-y,x+1/2,-z+1/2</tt>
<td>-4^-1<td>[0,0,1]<td>0,0,0<td>-1/4,1/4,1/4
</tr>
<tr>
<td><tt>-x,y+1/2,z+1/2</tt>
<td>-2<td>[1,0,0]<td>0,1/2,1/2<td>0,0,0
</tr>
<tr>
<td><tt>-y,-x+1/2,z+1/2</tt>
<td>-2<td>[1,1,0]<td>-1/4,1/4,1/2<td>1/4,0,0
</tr>
<tr>
<td><tt>x,-y+1/2,z+1/2</tt>
<td>-2<td>[0,1,0]<td>0,0,1/2<td>0,1/4,0
</tr>
<tr>
<td><tt>y,x+1/2,z+1/2</tt>
<td>-2<td>[-1,1,0]<td>1/4,1/4,1/2<td>-1/4,0,0
</tr>
<tr>
<td><tt>-z,-x+1/2,-y+1/2</tt>
<td>-3^1<td>[1,1,1]<td>0,0,0<td>0,1/2,0
</tr>
<tr>
<td><tt>x,-z+1/2,-y+1/2</tt>
<td>-2<td>[0,1,1]<td>0,0,0<td>0,1/2,0
</tr>
<tr>
<td><tt>z,x+1/2,-y+1/2</tt>
<td>-3^-1<td>[-1,1,1]<td>0,0,0<td>0,1/2,0
</tr>
<tr>
<td><tt>-x,z+1/2,-y+1/2</tt>
<td>-4^1<td>[1,0,0]<td>0,0,0<td>0,1/2,0
</tr>
<tr>
<td><tt>-z,x+1/2,y+1/2</tt>
<td>-3^-1<td>[1,-1,1]<td>0,0,0<td>-1/2,0,1/2
</tr>
<tr>
<td><tt>-x,-z+1/2,y+1/2</tt>
<td>-4^-1<td>[1,0,0]<td>0,0,0<td>0,0,1/2
</tr>
<tr>
<td><tt>z,-x+1/2,y+1/2</tt>
<td>-3^1<td>[-1,-1,1]<td>0,0,0<td>1/2,0,1/2
</tr>
<tr>
<td><tt>x,z+1/2,y+1/2</tt>
<td>-2<td>[0,-1,1]<td>0,1/2,1/2<td>0,0,0
</tr>
<tr>
<td><tt>-y,-z+1/2,-x+1/2</tt>
<td>-3^-1<td>[1,1,1]<td>0,0,0<td>0,0,1/2
</tr>
<tr>
<td><tt>-y,z+1/2,x+1/2</tt>
<td>-3^-1<td>[-1,-1,1]<td>0,0,0<td>-1/2,1/2,0
</tr>
<tr>
<td><tt>-z,-y+1/2,x+1/2</tt>
<td>-4^1<td>[0,1,0]<td>0,0,0<td>-1/4,1/4,1/4
</tr>
<tr>
<td><tt>y,-z+1/2,x+1/2</tt>
<td>-3^1<td>[-1,1,1]<td>0,0,0<td>0,0,1/2
</tr>
<tr>
<td><tt>z,y+1/2,x+1/2</tt>
<td>-2<td>[-1,0,1]<td>1/4,1/2,1/4<td>-1/4,0,0
</tr>
<tr>
<td><tt>y,z+1/2,-x+1/2</tt>
<td>-3^1<td>[1,-1,1]<td>0,0,0<td>1/2,1/2,0
</tr>
<tr>
<td><tt>-z,y+1/2,-x+1/2</tt>
<td>-2<td>[1,0,1]<td>-1/4,1/2,1/4<td>1/4,0,0
</tr>
<tr>
<td><tt>z,-y+1/2,-x+1/2</tt>
<td>-4^-1<td>[0,1,0]<td>0,0,0<td>1/4,1/4,1/4
</tr>
<tr>
<td><tt>x+1/2,y,z+1/2</tt>
<td>1<td>-<td>-<td>-
</tr>
<tr>
<td><tt>-y+1/2,x,z+1/2</tt>
<td>4^1<td>[0,0,1]<td>0,0,1/2<td>1/4,1/4,0
</tr>
<tr>
<td><tt>-x+1/2,-y,z+1/2</tt>
<td>2<td>[0,0,1]<td>0,0,1/2<td>1/4,0,0
</tr>
<tr>
<td><tt>y+1/2,-x,z+1/2</tt>
<td>4^-1<td>[0,0,1]<td>0,0,1/2<td>1/4,-1/4,0
</tr>
<tr>
<td><tt>x+1/2,-y,-z+1/2</tt>
<td>2<td>[1,0,0]<td>1/2,0,0<td>0,0,1/4
</tr>
<tr>
<td><tt>y+1/2,x,-z+1/2</tt>
<td>2<td>[1,1,0]<td>1/4,1/4,0<td>1/4,0,1/4
</tr>
<tr>
<td><tt>-x+1/2,y,-z+1/2</tt>
<td>2<td>[0,1,0]<td>0,0,0<td>1/4,0,1/4
</tr>
<tr>
<td><tt>-y+1/2,-x,-z+1/2</tt>
<td>2<td>[-1,1,0]<td>1/4,-1/4,0<td>1/4,0,1/4
</tr>
<tr>
<td><tt>z+1/2,x,y+1/2</tt>
<td>3^1<td>[1,1,1]<td>1/3,1/3,1/3<td>1/6,-1/6,0
</tr>
<tr>
<td><tt>-x+1/2,z,y+1/2</tt>
<td>2<td>[0,1,1]<td>0,1/4,1/4<td>1/4,-1/4,0
</tr>
<tr>
<td><tt>-z+1/2,-x,y+1/2</tt>
<td>3^-1<td>[-1,1,1]<td>0,0,0<td>1/2,-1/2,0
</tr>
<tr>
<td><tt>x+1/2,-z,y+1/2</tt>
<td>4^1<td>[1,0,0]<td>1/2,0,0<td>0,-1/4,1/4
</tr>
<tr>
<td><tt>z+1/2,-x,-y+1/2</tt>
<td>3^-1<td>[1,-1,1]<td>1/3,-1/3,1/3<td>1/6,1/6,0
</tr>
<tr>
<td><tt>x+1/2,z,-y+1/2</tt>
<td>4^-1<td>[1,0,0]<td>1/2,0,0<td>0,1/4,1/4
</tr>
<tr>
<td><tt>-z+1/2,x,-y+1/2</tt>
<td>3^1<td>[-1,-1,1]<td>0,0,0<td>1/2,1/2,0
</tr>
<tr>
<td><tt>-x+1/2,-z,-y+1/2</tt>
<td>2<td>[0,-1,1]<td>0,-1/4,1/4<td>1/4,1/4,0
</tr>
<tr>
<td><tt>y+1/2,z,x+1/2</tt>
<td>3^-1<td>[1,1,1]<td>1/3,1/3,1/3<td>-1/6,-1/3,0
</tr>
<tr>
<td><tt>y+1/2,-z,-x+1/2</tt>
<td>3^-1<td>[-1,-1,1]<td>0,0,0<td>1/2,0,0
</tr>
<tr>
<td><tt>z+1/2,y,-x+1/2</tt>
<td>4^1<td>[0,1,0]<td>0,0,0<td>1/2,0,0
</tr>
<tr>
<td><tt>-y+1/2,z,-x+1/2</tt>
<td>3^1<td>[-1,1,1]<td>0,0,0<td>1/2,0,0
</tr>
<tr>
<td><tt>-z+1/2,-y,-x+1/2</tt>
<td>2<td>[-1,0,1]<td>0,0,0<td>1/2,0,0
</tr>
<tr>
<td><tt>-y+1/2,-z,x+1/2</tt>
<td>3^1<td>[1,-1,1]<td>1/3,-1/3,1/3<td>-1/6,1/3,0
</tr>
<tr>
<td><tt>z+1/2,-y,x+1/2</tt>
<td>2<td>[1,0,1]<td>1/2,0,1/2<td>0,0,0
</tr>
<tr>
<td><tt>-z+1/2,y,x+1/2</tt>
<td>4^-1<td>[0,1,0]<td>0,0,0<td>0,0,1/2
</tr>
<tr>
<td><tt>-x+1/2,-y,-z+1/2</tt>
<td>-1<td>-<td>-<td>1/4,0,1/4
</tr>
<tr>
<td><tt>y+1/2,-x,-z+1/2</tt>
<td>-4^1<td>[0,0,1]<td>0,0,0<td>1/4,-1/4,1/4
</tr>
<tr>
<td><tt>x+1/2,y,-z+1/2</tt>
<td>-2<td>[0,0,1]<td>1/2,0,0<td>0,0,1/4
</tr>
<tr>
<td><tt>-y+1/2,x,-z+1/2</tt>
<td>-4^-1<td>[0,0,1]<td>0,0,0<td>1/4,1/4,1/4
</tr>
<tr>
<td><tt>-x+1/2,y,z+1/2</tt>
<td>-2<td>[1,0,0]<td>0,0,1/2<td>1/4,0,0
</tr>
<tr>
<td><tt>-y+1/2,-x,z+1/2</tt>
<td>-2<td>[1,1,0]<td>1/4,-1/4,1/2<td>1/4,0,0
</tr>
<tr>
<td><tt>x+1/2,-y,z+1/2</tt>
<td>-2<td>[0,1,0]<td>1/2,0,1/2<td>0,0,0
</tr>
<tr>
<td><tt>y+1/2,x,z+1/2</tt>
<td>-2<td>[-1,1,0]<td>1/4,1/4,1/2<td>1/4,0,0
</tr>
<tr>
<td><tt>-z+1/2,-x,-y+1/2</tt>
<td>-3^1<td>[1,1,1]<td>0,0,0<td>0,0,1/2
</tr>
<tr>
<td><tt>x+1/2,-z,-y+1/2</tt>
<td>-2<td>[0,1,1]<td>1/2,-1/4,1/4<td>0,1/4,0
</tr>
<tr>
<td><tt>z+1/2,x,-y+1/2</tt>
<td>-3^-1<td>[-1,1,1]<td>0,0,0<td>1/2,1/2,0
</tr>
<tr>
<td><tt>-x+1/2,z,-y+1/2</tt>
<td>-4^1<td>[1,0,0]<td>0,0,0<td>1/4,1/4,1/4
</tr>
<tr>
<td><tt>-z+1/2,x,y+1/2</tt>
<td>-3^-1<td>[1,-1,1]<td>0,0,0<td>0,0,1/2
</tr>
<tr>
<td><tt>-x+1/2,-z,y+1/2</tt>
<td>-4^-1<td>[1,0,0]<td>0,0,0<td>1/4,-1/4,1/4
</tr>
<tr>
<td><tt>z+1/2,-x,y+1/2</tt>
<td>-3^1<td>[-1,-1,1]<td>0,0,0<td>1/2,-1/2,0
</tr>
<tr>
<td><tt>x+1/2,z,y+1/2</tt>
<td>-2<td>[0,-1,1]<td>1/2,1/4,1/4<td>0,-1/4,0
</tr>
<tr>
<td><tt>-y+1/2,-z,-x+1/2</tt>
<td>-3^-1<td>[1,1,1]<td>0,0,0<td>1/2,0,0
</tr>
<tr>
<td><tt>-y+1/2,z,x+1/2</tt>
<td>-3^-1<td>[-1,-1,1]<td>0,0,0<td>0,1/2,1/2
</tr>
<tr>
<td><tt>-z+1/2,-y,x+1/2</tt>
<td>-4^1<td>[0,1,0]<td>0,0,0<td>0,0,1/2
</tr>
<tr>
<td><tt>y+1/2,-z,x+1/2</tt>
<td>-3^1<td>[-1,1,1]<td>0,0,0<td>0,-1/2,1/2
</tr>
<tr>
<td><tt>z+1/2,y,x+1/2</tt>
<td>-2<td>[-1,0,1]<td>1/2,0,1/2<td>0,0,0
</tr>
<tr>
<td><tt>y+1/2,z,-x+1/2</tt>
<td>-3^1<td>[1,-1,1]<td>0,0,0<td>1/2,0,0
</tr>
<tr>
<td><tt>-z+1/2,y,-x+1/2</tt>
<td>-2<td>[1,0,1]<td>0,0,0<td>1/2,0,0
</tr>
<tr>
<td><tt>z+1/2,-y,-x+1/2</tt>
<td>-4^-1<td>[0,1,0]<td>0,0,0<td>1/2,0,0
</tr>
<tr>
<td><tt>x+1/2,y+1/2,z</tt>
<td>1<td>-<td>-<td>-
</tr>
<tr>
<td><tt>-y+1/2,x+1/2,z</tt>
<td>4^1<td>[0,0,1]<td>0,0,0<td>0,1/2,0
</tr>
<tr>
<td><tt>-x+1/2,-y+1/2,z</tt>
<td>2<td>[0,0,1]<td>0,0,0<td>1/4,1/4,0
</tr>
<tr>
<td><tt>y+1/2,-x+1/2,z</tt>
<td>4^-1<td>[0,0,1]<td>0,0,0<td>1/2,0,0
</tr>
<tr>
<td><tt>x+1/2,-y+1/2,-z</tt>
<td>2<td>[1,0,0]<td>1/2,0,0<td>0,1/4,0
</tr>
<tr>
<td><tt>y+1/2,x+1/2,-z</tt>
<td>2<td>[1,1,0]<td>1/2,1/2,0<td>0,0,0
</tr>
<tr>
<td><tt>-x+1/2,y+1/2,-z</tt>
<td>2<td>[0,1,0]<td>0,1/2,0<td>1/4,0,0
</tr>
<tr>
<td><tt>-y+1/2,-x+1/2,-z</tt>
<td>2<td>[-1,1,0]<td>0,0,0<td>1/2,0,0
</tr>
<tr>
<td><tt>z+1/2,x+1/2,y</tt>
<td>3^1<td>[1,1,1]<td>1/3,1/3,1/3<td>1/6,1/3,0
</tr>
<tr>
<td><tt>-x+1/2,z+1/2,y</tt>
<td>2<td>[0,1,1]<td>0,1/4,1/4<td>1/4,1/4,0
</tr>
<tr>
<td><tt>-z+1/2,-x+1/2,y</tt>
<td>3^-1<td>[-1,1,1]<td>0,0,0<td>1/2,0,0
</tr>
<tr>
<td><tt>x+1/2,-z+1/2,y</tt>
<td>4^1<td>[1,0,0]<td>1/2,0,0<td>0,1/4,1/4
</tr>
<tr>
<td><tt>z+1/2,-x+1/2,-y</tt>
<td>3^-1<td>[1,-1,1]<td>0,0,0<td>1/2,0,0
</tr>
<tr>
<td><tt>x+1/2,z+1/2,-y</tt>
<td>4^-1<td>[1,0,0]<td>1/2,0,0<td>0,1/4,-1/4
</tr>
<tr>
<td><tt>-z+1/2,x+1/2,-y</tt>
<td>3^1<td>[-1,-1,1]<td>1/3,1/3,-1/3<td>1/6,1/3,0
</tr>
<tr>
<td><tt>-x+1/2,-z+1/2,-y</tt>
<td>2<td>[0,-1,1]<td>0,1/4,-1/4<td>1/4,1/4,0
</tr>
<tr>
<td><tt>y+1/2,z+1/2,x</tt>
<td>3^-1<td>[1,1,1]<td>1/3,1/3,1/3<td>1/3,1/6,0
</tr>
<tr>
<td><tt>y+1/2,-z+1/2,-x</tt>
<td>3^-1<td>[-1,-1,1]<td>1/3,1/3,-1/3<td>1/3,1/6,0
</tr>
<tr>
<td><tt>z+1/2,y+1/2,-x</tt>
<td>4^1<td>[0,1,0]<td>0,1/2,0<td>1/4,0,-1/4
</tr>
<tr>
<td><tt>-y+1/2,z+1/2,-x</tt>
<td>3^1<td>[-1,1,1]<td>0,0,0<td>0,1/2,0
</tr>
<tr>
<td><tt>-z+1/2,-y+1/2,-x</tt>
<td>2<td>[-1,0,1]<td>1/4,0,-1/4<td>1/4,1/4,0
</tr>
<tr>
<td><tt>-y+1/2,-z+1/2,x</tt>
<td>3^1<td>[1,-1,1]<td>0,0,0<td>0,1/2,0
</tr>
<tr>
<td><tt>z+1/2,-y+1/2,x</tt>
<td>2<td>[1,0,1]<td>1/4,0,1/4<td>1/4,1/4,0
</tr>
<tr>
<td><tt>-z+1/2,y+1/2,x</tt>
<td>4^-1<td>[0,1,0]<td>0,1/2,0<td>1/4,0,1/4
</tr>
<tr>
<td><tt>-x+1/2,-y+1/2,-z</tt>
<td>-1<td>-<td>-<td>1/4,1/4,0
</tr>
<tr>
<td><tt>y+1/2,-x+1/2,-z</tt>
<td>-4^1<td>[0,0,1]<td>0,0,0<td>1/2,0,0
</tr>
<tr>
<td><tt>x+1/2,y+1/2,-z</tt>
<td>-2<td>[0,0,1]<td>1/2,1/2,0<td>0,0,0
</tr>
<tr>
<td><tt>-y+1/2,x+1/2,-z</tt>
<td>-4^-1<td>[0,0,1]<td>0,0,0<td>0,1/2,0
</tr>
<tr>
<td><tt>-x+1/2,y+1/2,z</tt>
<td>-2<td>[1,0,0]<td>0,1/2,0<td>1/4,0,0
</tr>
<tr>
<td><tt>-y+1/2,-x+1/2,z</tt>
<td>-2<td>[1,1,0]<td>0,0,0<td>1/2,0,0
</tr>
<tr>
<td><tt>x+1/2,-y+1/2,z</tt>
<td>-2<td>[0,1,0]<td>1/2,0,0<td>0,1/4,0
</tr>
<tr>
<td><tt>y+1/2,x+1/2,z</tt>
<td>-2<td>[-1,1,0]<td>1/2,1/2,0<td>0,0,0
</tr>
<tr>
<td><tt>-z+1/2,-x+1/2,-y</tt>
<td>-3^1<td>[1,1,1]<td>0,0,0<td>1/2,0,0
</tr>
<tr>
<td><tt>x+1/2,-z+1/2,-y</tt>
<td>-2<td>[0,1,1]<td>1/2,1/4,-1/4<td>0,1/4,0
</tr>
<tr>
<td><tt>z+1/2,x+1/2,-y</tt>
<td>-3^-1<td>[-1,1,1]<td>0,0,0<td>0,1/2,-1/2
</tr>
<tr>
<td><tt>-x+1/2,z+1/2,-y</tt>
<td>-4^1<td>[1,0,0]<td>0,0,0<td>1/4,1/4,-1/4
</tr>
<tr>
<td><tt>-z+1/2,x+1/2,y</tt>
<td>-3^-1<td>[1,-1,1]<td>0,0,0<td>0,1/2,1/2
</tr>
<tr>
<td><tt>-x+1/2,-z+1/2,y</tt>
<td>-4^-1<td>[1,0,0]<td>0,0,0<td>1/4,1/4,1/4
</tr>
<tr>
<td><tt>z+1/2,-x+1/2,y</tt>
<td>-3^1<td>[-1,-1,1]<td>0,0,0<td>1/2,0,0
</tr>
<tr>
<td><tt>x+1/2,z+1/2,y</tt>
<td>-2<td>[0,-1,1]<td>1/2,1/4,1/4<td>0,1/4,0
</tr>
<tr>
<td><tt>-y+1/2,-z+1/2,-x</tt>
<td>-3^-1<td>[1,1,1]<td>0,0,0<td>0,1/2,0
</tr>
<tr>
<td><tt>-y+1/2,z+1/2,x</tt>
<td>-3^-1<td>[-1,-1,1]<td>0,0,0<td>0,1/2,0
</tr>
<tr>
<td><tt>-z+1/2,-y+1/2,x</tt>
<td>-4^1<td>[0,1,0]<td>0,0,0<td>1/4,1/4,1/4
</tr>
<tr>
<td><tt>y+1/2,-z+1/2,x</tt>
<td>-3^1<td>[-1,1,1]<td>0,0,0<td>1/2,0,1/2
</tr>
<tr>
<td><tt>z+1/2,y+1/2,x</tt>
<td>-2<td>[-1,0,1]<td>1/4,1/2,1/4<td>1/4,0,0
</tr>
<tr>
<td><tt>y+1/2,z+1/2,-x</tt>
<td>-3^1<td>[1,-1,1]<td>0,0,0<td>1/2,0,-1/2
</tr>
<tr>
<td><tt>-z+1/2,y+1/2,-x</tt>
<td>-2<td>[1,0,1]<td>1/4,1/2,-1/4<td>1/4,0,0
</tr>
<tr>
<td><tt>z+1/2,-y+1/2,-x</tt>
<td>-4^-1<td>[0,1,0]<td>0,0,0<td>1/4,1/4,-1/4
</tr>
</table><pre>

List of Wyckoff positions:
</pre><table border=2 cellpadding=2>
<tr>
<th>Wyckoff letter
<th>Multiplicity
<th>Site symmetry<br>point group type
<th>Representative special position operator
</tr>
<tr>
<td>l<td>192<td>1<td><tt>x,y,z</tt>
</tr>
<tr>
<td>k<td>96<td>m<td><tt>x,x,z</tt>
</tr>
<tr>
<td>j<td>96<td>m<td><tt>0,y,z</tt>
</tr>
<tr>
<td>i<td>48<td>mm2<td><tt>1/2,y,y</tt>
</tr>
<tr>
<td>h<td>48<td>mm2<td><tt>0,y,y</tt>
</tr>
<tr>
<td>g<td>48<td>mm2<td><tt>x,1/4,1/4</tt>
</tr>
<tr>
<td>f<td>32<td>3m<td><tt>x,x,x</tt>
</tr>
<tr>
<td>e<td>24<td>4mm<td><tt>x,0,0</tt>
</tr>
<tr>
<td>d<td>24<td>mmm<td><tt>0,1/4,1/4</tt>
</tr>
<tr>
<td>c<td>8<td>-43m<td><tt>1/4,1/4,1/4</tt>
</tr>
<tr>
<td>b<td>4<td>m-3m<td><tt>1/2,1/2,1/2</tt>
</tr>
<tr>
<td>a<td>4<td>m-3m<td><tt>0,0,0</tt>
</tr>
</table><pre>

Harker planes:
</pre><table border=2 cellpadding=2>
<tr>
<th>Algebraic
<th>Normal vector
<th>A point in the plane
</tr>
<tr>
<td><tt>x-y,-x-y,0</tt><td>[0,0,1]<td>0,0,0
</tr>
<tr>
<td><tt>0,2*y,2*z</tt><td>[1,0,0]<td>0,0,0
</tr>
<tr>
<td><tt>x+y,-x-y,2*z</tt><td>[1,1,0]<td>0,0,0
</tr>
<tr>
<td><tt>2*x,0,2*z</tt><td>[0,1,0]<td>0,0,0
</tr>
<tr>
<td><tt>x+y,x+y,2*z</tt><td>[-1,1,0]<td>0,0,0
</tr>
<tr>
<td><tt>x+z,-x-y,y-z</tt><td>[1,1,1]<td>0,0,0
</tr>
<tr>
<td><tt>2*x,y+z,-y-z</tt><td>[0,1,1]<td>0,0,0
</tr>
<tr>
<td><tt>x+z,-x-y,-y+z</tt><td>[-1,-1,1]<td>0,0,0
</tr>
<tr>
<td><tt>2*x,y+z,y+z</tt><td>[0,-1,1]<td>0,0,0
</tr>
<tr>
<td><tt>x+y,y-z,x+z</tt><td>[-1,1,1]<td>0,0,0
</tr>
<tr>
<td><tt>x+z,2*y,x+z</tt><td>[-1,0,1]<td>0,0,0
</tr>
<tr>
<td><tt>x+y,y-z,-x-z</tt><td>[1,-1,1]<td>0,0,0
</tr>
<tr>
<td><tt>x+z,2*y,-x-z</tt><td>[1,0,1]<td>0,0,0
</tr>
</table><pre>

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: (2, 2, 2)
  Structure-seminvariant vectors and moduli: (2, 1, 1)
  Euclidean normalizer: (2, 2, 2)

  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.

</pre>
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