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<hr>
<pre>
Result of symbol lookup:
  Space group number: 227
  Schoenflies symbol: Oh^7
  Hermann-Mauguin symbol: F d -3 m
  Origin choice: 2
  Hall symbol: -F 4vw 2vw 3

Input space group symbol: F d -3 m :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&lt;=x&lt;=1/8; 0&lt;=y&lt;=1/8; 0&lt;=z&lt;1

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+1/4,z+1/4</tt>
<td>4^1<td>[0,0,1]<td>0,0,1/4<td>-1/8,1/8,0
</tr>
<tr>
<td><tt>-x+3/4,-y+1/4,z+1/2</tt>
<td>2<td>[0,0,1]<td>0,0,1/2<td>3/8,1/8,0
</tr>
<tr>
<td><tt>y+3/4,-x,z+3/4</tt>
<td>4^-1<td>[0,0,1]<td>0,0,3/4<td>3/8,-3/8,0
</tr>
<tr>
<td><tt>x,-y+1/4,-z+1/4</tt>
<td>2<td>[1,0,0]<td>0,0,0<td>0,1/8,1/8
</tr>
<tr>
<td><tt>y+3/4,x+1/4,-z+1/2</tt>
<td>2<td>[1,1,0]<td>1/2,1/2,0<td>1/4,0,1/4
</tr>
<tr>
<td><tt>-x+3/4,y,-z+3/4</tt>
<td>2<td>[0,1,0]<td>0,0,0<td>3/8,0,3/8
</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+1/4,y+1/4</tt>
<td>2<td>[0,1,1]<td>0,1/4,1/4<td>0,0,0
</tr>
<tr>
<td><tt>-z+3/4,-x+1/4,y+1/2</tt>
<td>3^-1<td>[-1,1,1]<td>0,0,0<td>3/4,-1/2,0
</tr>
<tr>
<td><tt>x+3/4,-z,y+3/4</tt>
<td>4^1<td>[1,0,0]<td>3/4,0,0<td>0,-3/8,3/8
</tr>
<tr>
<td><tt>z,-x+1/4,-y+1/4</tt>
<td>3^-1<td>[1,-1,1]<td>0,0,0<td>0,1/4,0
</tr>
<tr>
<td><tt>x+3/4,z+1/4,-y+1/2</tt>
<td>4^-1<td>[1,0,0]<td>3/4,0,0<td>0,3/8,1/8
</tr>
<tr>
<td><tt>-z+3/4,x,-y+3/4</tt>
<td>3^1<td>[-1,-1,1]<td>0,0,0<td>3/4,3/4,0
</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+1/2,-z+3/4,-x+1/4</tt>
<td>3^-1<td>[-1,-1,1]<td>1/3,1/3,-1/3<td>7/12,5/12,0
</tr>
<tr>
<td><tt>z+1/4,y+3/4,-x+1/2</tt>
<td>4^1<td>[0,1,0]<td>0,3/4,0<td>3/8,0,1/8
</tr>
<tr>
<td><tt>-y+1/4,z+1/2,-x+3/4</tt>
<td>3^1<td>[-1,1,1]<td>-1/3,1/3,1/3<td>5/12,1/6,0
</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+1/4,-z+1/4,x</tt>
<td>3^1<td>[1,-1,1]<td>0,0,0<td>0,1/4,0
</tr>
<tr>
<td><tt>z+1/4,-y,x+1/4</tt>
<td>2<td>[1,0,1]<td>1/4,0,1/4<td>0,0,0
</tr>
<tr>
<td><tt>-z+1/2,y+1/4,x+3/4</tt>
<td>4^-1<td>[0,1,0]<td>0,1/4,0<td>-1/8,0,5/8
</tr>
<tr>
<td><tt>-x,-y,-z</tt>
<td>-1<td>-<td>-<td>0,0,0
</tr>
<tr>
<td><tt>y,-x-1/4,-z-1/4</tt>
<td>-4^1<td>[0,0,1]<td>0,0,0<td>-1/8,-1/8,-1/8
</tr>
<tr>
<td><tt>x-3/4,y-1/4,-z-1/2</tt>
<td>-2<td>[0,0,1]<td>-3/4,-1/4,0<td>0,0,-1/4
</tr>
<tr>
<td><tt>-y-3/4,x,-z-3/4</tt>
<td>-4^-1<td>[0,0,1]<td>0,0,0<td>-3/8,-3/8,-3/8
</tr>
<tr>
<td><tt>-x,y-1/4,z-1/4</tt>
<td>-2<td>[1,0,0]<td>0,-1/4,-1/4<td>0,0,0
</tr>
<tr>
<td><tt>-y-3/4,-x-1/4,z-1/2</tt>
<td>-2<td>[1,1,0]<td>-1/4,1/4,-1/2<td>-1/2,0,0
</tr>
<tr>
<td><tt>x-3/4,-y,z-3/4</tt>
<td>-2<td>[0,1,0]<td>-3/4,0,-3/4<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-1/4,-y-1/4</tt>
<td>-2<td>[0,1,1]<td>0,0,0<td>0,-1/4,0
</tr>
<tr>
<td><tt>z-3/4,x-1/4,-y-1/2</tt>
<td>-3^-1<td>[-1,1,1]<td>0,0,0<td>-1/2,-3/4,1/4
</tr>
<tr>
<td><tt>-x-3/4,z,-y-3/4</tt>
<td>-4^1<td>[1,0,0]<td>0,0,0<td>-3/8,-3/8,-3/8
</tr>
<tr>
<td><tt>-z,x-1/4,y-1/4</tt>
<td>-3^-1<td>[1,-1,1]<td>0,0,0<td>1/4,0,-1/4
</tr>
<tr>
<td><tt>-x-3/4,-z-1/4,y-1/2</tt>
<td>-4^-1<td>[1,0,0]<td>0,0,0<td>-3/8,1/8,-3/8
</tr>
<tr>
<td><tt>z-3/4,-x,y-3/4</tt>
<td>-3^1<td>[-1,-1,1]<td>0,0,0<td>-3/4,3/4,0
</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-1/2,z-3/4,x-1/4</tt>
<td>-3^-1<td>[-1,-1,1]<td>0,0,0<td>1/4,-3/4,0
</tr>
<tr>
<td><tt>-z-1/4,-y-3/4,x-1/2</tt>
<td>-4^1<td>[0,1,0]<td>0,0,0<td>1/8,-3/8,-3/8
</tr>
<tr>
<td><tt>y-1/4,-z-1/2,x-3/4</tt>
<td>-3^1<td>[-1,1,1]<td>0,0,0<td>0,1/4,-3/4
</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-1/4,z-1/4,-x</tt>
<td>-3^1<td>[1,-1,1]<td>0,0,0<td>-1/4,0,1/4
</tr>
<tr>
<td><tt>-z-1/4,y,-x-1/4</tt>
<td>-2<td>[1,0,1]<td>0,0,0<td>-1/4,0,0
</tr>
<tr>
<td><tt>z-1/2,-y-1/4,-x-3/4</tt>
<td>-4^-1<td>[0,1,0]<td>0,0,0<td>-5/8,-1/8,-1/8
</tr>
<tr>
<td><tt>x,y+1/2,z+1/2</tt>
<td>1<td>-<td>-<td>-
</tr>
<tr>
<td><tt>-y,x+3/4,z+3/4</tt>
<td>4^1<td>[0,0,1]<td>0,0,3/4<td>-3/8,3/8,0
</tr>
<tr>
<td><tt>-x+3/4,-y+3/4,z+1</tt>
<td>2<td>[0,0,1]<td>0,0,1<td>3/8,3/8,0
</tr>
<tr>
<td><tt>y+3/4,-x+1/2,z+5/4</tt>
<td>4^-1<td>[0,0,1]<td>0,0,5/4<td>5/8,-1/8,0
</tr>
<tr>
<td><tt>x,-y+3/4,-z+3/4</tt>
<td>2<td>[1,0,0]<td>0,0,0<td>0,3/8,3/8
</tr>
<tr>
<td><tt>y+3/4,x+3/4,-z+1</tt>
<td>2<td>[1,1,0]<td>3/4,3/4,0<td>0,0,1/2
</tr>
<tr>
<td><tt>-x+3/4,y+1/2,-z+5/4</tt>
<td>2<td>[0,1,0]<td>0,1/2,0<td>3/8,0,5/8
</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+3/4,y+3/4</tt>
<td>2<td>[0,1,1]<td>0,3/4,3/4<td>0,0,0
</tr>
<tr>
<td><tt>-z+3/4,-x+3/4,y+1</tt>
<td>3^-1<td>[-1,1,1]<td>-1/3,1/3,1/3<td>13/12,-2/3,0
</tr>
<tr>
<td><tt>x+3/4,-z+1/2,y+5/4</tt>
<td>4^1<td>[1,0,0]<td>3/4,0,0<td>0,-3/8,7/8
</tr>
<tr>
<td><tt>z,-x+3/4,-y+3/4</tt>
<td>3^-1<td>[1,-1,1]<td>0,0,0<td>0,3/4,0
</tr>
<tr>
<td><tt>x+3/4,z+3/4,-y+1</tt>
<td>4^-1<td>[1,0,0]<td>3/4,0,0<td>0,7/8,1/8
</tr>
<tr>
<td><tt>-z+3/4,x+1/2,-y+5/4</tt>
<td>3^1<td>[-1,-1,1]<td>0,0,0<td>3/4,5/4,0
</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+1/2,-z+5/4,-x+3/4</tt>
<td>3^-1<td>[-1,-1,1]<td>1/3,1/3,-1/3<td>13/12,11/12,0
</tr>
<tr>
<td><tt>z+1/4,y+5/4,-x+1</tt>
<td>4^1<td>[0,1,0]<td>0,5/4,0<td>5/8,0,3/8
</tr>
<tr>
<td><tt>-y+1/4,z+1,-x+5/4</tt>
<td>3^1<td>[-1,1,1]<td>-2/3,2/3,2/3<td>7/12,1/3,0
</tr>
<tr>
<td><tt>-z,-y+1,-x+1</tt>
<td>2<td>[-1,0,1]<td>-1/2,0,1/2<td>1/2,1/2,0
</tr>
<tr>
<td><tt>-y+1/4,-z+3/4,x+1/2</tt>
<td>3^1<td>[1,-1,1]<td>0,0,0<td>-1/2,3/4,0
</tr>
<tr>
<td><tt>z+1/4,-y+1/2,x+3/4</tt>
<td>2<td>[1,0,1]<td>1/2,0,1/2<td>-1/4,1/4,0
</tr>
<tr>
<td><tt>-z+1/2,y+3/4,x+5/4</tt>
<td>4^-1<td>[0,1,0]<td>0,3/4,0<td>-3/8,0,7/8
</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+1/4,-z+1/4</tt>
<td>-4^1<td>[0,0,1]<td>0,0,0<td>1/8,1/8,1/8
</tr>
<tr>
<td><tt>x-3/4,y+1/4,-z</tt>
<td>-2<td>[0,0,1]<td>-3/4,1/4,0<td>0,0,0
</tr>
<tr>
<td><tt>-y-3/4,x+1/2,-z-1/4</tt>
<td>-4^-1<td>[0,0,1]<td>0,0,0<td>-5/8,-1/8,-1/8
</tr>
<tr>
<td><tt>-x,y+1/4,z+1/4</tt>
<td>-2<td>[1,0,0]<td>0,1/4,1/4<td>0,0,0
</tr>
<tr>
<td><tt>-y-3/4,-x+1/4,z</tt>
<td>-2<td>[1,1,0]<td>-1/2,1/2,0<td>-1/4,0,0
</tr>
<tr>
<td><tt>x-3/4,-y+1/2,z-1/4</tt>
<td>-2<td>[0,1,0]<td>-3/4,0,-1/4<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+1/4,-y+1/4</tt>
<td>-2<td>[0,1,1]<td>0,0,0<td>0,1/4,0
</tr>
<tr>
<td><tt>z-3/4,x+1/4,-y</tt>
<td>-3^-1<td>[-1,1,1]<td>0,0,0<td>-1/2,-1/4,1/4
</tr>
<tr>
<td><tt>-x-3/4,z+1/2,-y-1/4</tt>
<td>-4^1<td>[1,0,0]<td>0,0,0<td>-3/8,1/8,-3/8
</tr>
<tr>
<td><tt>-z,x+1/4,y+1/4</tt>
<td>-3^-1<td>[1,-1,1]<td>0,0,0<td>-1/4,0,1/4
</tr>
<tr>
<td><tt>-x-3/4,-z+1/4,y</tt>
<td>-4^-1<td>[1,0,0]<td>0,0,0<td>-3/8,1/8,1/8
</tr>
<tr>
<td><tt>z-3/4,-x+1/2,y-1/4</tt>
<td>-3^1<td>[-1,-1,1]<td>0,0,0<td>-1/4,3/4,1/2
</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-1/2,z-1/4,x+1/4</tt>
<td>-3^-1<td>[-1,-1,1]<td>0,0,0<td>-1/4,-1/4,0
</tr>
<tr>
<td><tt>-z-1/4,-y-1/4,x</tt>
<td>-4^1<td>[0,1,0]<td>0,0,0<td>-1/8,-1/8,-1/8
</tr>
<tr>
<td><tt>y-1/4,-z,x-1/4</tt>
<td>-3^1<td>[-1,1,1]<td>0,0,0<td>0,1/4,-1/4
</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-1/4,z+1/4,-x+1/2</tt>
<td>-3^1<td>[1,-1,1]<td>0,0,0<td>1/4,1/2,1/4
</tr>
<tr>
<td><tt>-z-1/4,y+1/2,-x+1/4</tt>
<td>-2<td>[1,0,1]<td>-1/4,1/2,1/4<td>0,0,0
</tr>
<tr>
<td><tt>z-1/2,-y+1/4,-x-1/4</tt>
<td>-4^-1<td>[0,1,0]<td>0,0,0<td>-3/8,1/8,1/8
</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+1/4,z+3/4</tt>
<td>4^1<td>[0,0,1]<td>0,0,3/4<td>1/8,3/8,0
</tr>
<tr>
<td><tt>-x+5/4,-y+1/4,z+1</tt>
<td>2<td>[0,0,1]<td>0,0,1<td>5/8,1/8,0
</tr>
<tr>
<td><tt>y+5/4,-x,z+5/4</tt>
<td>4^-1<td>[0,0,1]<td>0,0,5/4<td>5/8,-5/8,0
</tr>
<tr>
<td><tt>x+1/2,-y+1/4,-z+3/4</tt>
<td>2<td>[1,0,0]<td>1/2,0,0<td>0,1/8,3/8
</tr>
<tr>
<td><tt>y+5/4,x+1/4,-z+1</tt>
<td>2<td>[1,1,0]<td>3/4,3/4,0<td>1/2,0,1/2
</tr>
<tr>
<td><tt>-x+5/4,y,-z+5/4</tt>
<td>2<td>[0,1,0]<td>0,0,0<td>5/8,0,5/8
</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+1/4,y+3/4</tt>
<td>2<td>[0,1,1]<td>0,1/2,1/2<td>1/4,-1/4,0
</tr>
<tr>
<td><tt>-z+5/4,-x+1/4,y+1</tt>
<td>3^-1<td>[-1,1,1]<td>0,0,0<td>5/4,-1,0
</tr>
<tr>
<td><tt>x+5/4,-z,y+5/4</tt>
<td>4^1<td>[1,0,0]<td>5/4,0,0<td>0,-5/8,5/8
</tr>
<tr>
<td><tt>z+1/2,-x+1/4,-y+3/4</tt>
<td>3^-1<td>[1,-1,1]<td>1/3,-1/3,1/3<td>1/6,5/12,0
</tr>
<tr>
<td><tt>x+5/4,z+1/4,-y+1</tt>
<td>4^-1<td>[1,0,0]<td>5/4,0,0<td>0,5/8,3/8
</tr>
<tr>
<td><tt>-z+5/4,x,-y+5/4</tt>
<td>3^1<td>[-1,-1,1]<td>0,0,0<td>5/4,5/4,0
</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,-z+3/4,-x+3/4</tt>
<td>3^-1<td>[-1,-1,1]<td>1/3,1/3,-1/3<td>13/12,5/12,0
</tr>
<tr>
<td><tt>z+3/4,y+3/4,-x+1</tt>
<td>4^1<td>[0,1,0]<td>0,3/4,0<td>7/8,0,1/8
</tr>
<tr>
<td><tt>-y+3/4,z+1/2,-x+5/4</tt>
<td>3^1<td>[-1,1,1]<td>-1/3,1/3,1/3<td>11/12,1/6,0
</tr>
<tr>
<td><tt>-z+1/2,-y+1/2,-x+1</tt>
<td>2<td>[-1,0,1]<td>-1/4,0,1/4<td>3/4,1/4,0
</tr>
<tr>
<td><tt>-y+3/4,-z+1/4,x+1/2</tt>
<td>3^1<td>[1,-1,1]<td>1/3,-1/3,1/3<td>-1/6,7/12,0
</tr>
<tr>
<td><tt>z+3/4,-y,x+3/4</tt>
<td>2<td>[1,0,1]<td>3/4,0,3/4<td>0,0,0
</tr>
<tr>
<td><tt>-z+1,y+1/4,x+5/4</tt>
<td>4^-1<td>[0,1,0]<td>0,1/4,0<td>-1/8,0,9/8
</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-1/4,-z+1/4</tt>
<td>-4^1<td>[0,0,1]<td>0,0,0<td>1/8,-3/8,1/8
</tr>
<tr>
<td><tt>x-1/4,y-1/4,-z</tt>
<td>-2<td>[0,0,1]<td>-1/4,-1/4,0<td>0,0,0
</tr>
<tr>
<td><tt>-y-1/4,x,-z-1/4</tt>
<td>-4^-1<td>[0,0,1]<td>0,0,0<td>-1/8,-1/8,-1/8
</tr>
<tr>
<td><tt>-x+1/2,y-1/4,z+1/4</tt>
<td>-2<td>[1,0,0]<td>0,-1/4,1/4<td>1/4,0,0
</tr>
<tr>
<td><tt>-y-1/4,-x-1/4,z</tt>
<td>-2<td>[1,1,0]<td>0,0,0<td>-1/4,0,0
</tr>
<tr>
<td><tt>x-1/4,-y,z-1/4</tt>
<td>-2<td>[0,1,0]<td>-1/4,0,-1/4<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-1/4,-y+1/4</tt>
<td>-2<td>[0,1,1]<td>1/2,-1/4,1/4<td>0,0,0
</tr>
<tr>
<td><tt>z-1/4,x-1/4,-y</tt>
<td>-3^-1<td>[-1,1,1]<td>0,0,0<td>0,-1/4,1/4
</tr>
<tr>
<td><tt>-x-1/4,z,-y-1/4</tt>
<td>-4^1<td>[1,0,0]<td>0,0,0<td>-1/8,-1/8,-1/8
</tr>
<tr>
<td><tt>-z+1/2,x-1/4,y+1/4</tt>
<td>-3^-1<td>[1,-1,1]<td>0,0,0<td>1/4,0,1/4
</tr>
<tr>
<td><tt>-x-1/4,-z-1/4,y</tt>
<td>-4^-1<td>[1,0,0]<td>0,0,0<td>-1/8,-1/8,-1/8
</tr>
<tr>
<td><tt>z-1/4,-x,y-1/4</tt>
<td>-3^1<td>[-1,-1,1]<td>0,0,0<td>-1/4,1/4,0
</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,z-3/4,x+1/4</tt>
<td>-3^-1<td>[-1,-1,1]<td>0,0,0<td>1/4,-1/4,1/2
</tr>
<tr>
<td><tt>-z+1/4,-y-3/4,x</tt>
<td>-4^1<td>[0,1,0]<td>0,0,0<td>1/8,-3/8,1/8
</tr>
<tr>
<td><tt>y+1/4,-z-1/2,x-1/4</tt>
<td>-3^1<td>[-1,1,1]<td>0,0,0<td>0,-1/4,-1/4
</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+1/4,z-1/4,-x+1/2</tt>
<td>-3^1<td>[1,-1,1]<td>0,0,0<td>1/4,0,1/4
</tr>
<tr>
<td><tt>-z+1/4,y,-x+1/4</tt>
<td>-2<td>[1,0,1]<td>0,0,0<td>1/4,0,0
</tr>
<tr>
<td><tt>z,-y-1/4,-x-1/4</tt>
<td>-4^-1<td>[0,1,0]<td>0,0,0<td>-1/8,-1/8,-1/8
</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+3/4,z+1/4</tt>
<td>4^1<td>[0,0,1]<td>0,0,1/4<td>-1/8,5/8,0
</tr>
<tr>
<td><tt>-x+5/4,-y+3/4,z+1/2</tt>
<td>2<td>[0,0,1]<td>0,0,1/2<td>5/8,3/8,0
</tr>
<tr>
<td><tt>y+5/4,-x+1/2,z+3/4</tt>
<td>4^-1<td>[0,0,1]<td>0,0,3/4<td>7/8,-3/8,0
</tr>
<tr>
<td><tt>x+1/2,-y+3/4,-z+1/4</tt>
<td>2<td>[1,0,0]<td>1/2,0,0<td>0,3/8,1/8
</tr>
<tr>
<td><tt>y+5/4,x+3/4,-z+1/2</tt>
<td>2<td>[1,1,0]<td>1,1,0<td>1/4,0,1/4
</tr>
<tr>
<td><tt>-x+5/4,y+1/2,-z+3/4</tt>
<td>2<td>[0,1,0]<td>0,1/2,0<td>5/8,0,3/8
</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+3/4,y+1/4</tt>
<td>2<td>[0,1,1]<td>0,1/2,1/2<td>1/4,1/4,0
</tr>
<tr>
<td><tt>-z+5/4,-x+3/4,y+1/2</tt>
<td>3^-1<td>[-1,1,1]<td>0,0,0<td>5/4,-1/2,0
</tr>
<tr>
<td><tt>x+5/4,-z+1/2,y+3/4</tt>
<td>4^1<td>[1,0,0]<td>5/4,0,0<td>0,-1/8,5/8
</tr>
<tr>
<td><tt>z+1/2,-x+3/4,-y+1/4</tt>
<td>3^-1<td>[1,-1,1]<td>0,0,0<td>1/2,1/4,0
</tr>
<tr>
<td><tt>x+5/4,z+3/4,-y+1/2</tt>
<td>4^-1<td>[1,0,0]<td>5/4,0,0<td>0,5/8,-1/8
</tr>
<tr>
<td><tt>-z+5/4,x+1/2,-y+3/4</tt>
<td>3^1<td>[-1,-1,1]<td>1/3,1/3,-1/3<td>11/12,13/12,0
</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,-z+5/4,-x+1/4</tt>
<td>3^-1<td>[-1,-1,1]<td>2/3,2/3,-2/3<td>11/12,7/12,0
</tr>
<tr>
<td><tt>z+3/4,y+5/4,-x+1/2</tt>
<td>4^1<td>[0,1,0]<td>0,5/4,0<td>5/8,0,-1/8
</tr>
<tr>
<td><tt>-y+3/4,z+1,-x+3/4</tt>
<td>3^1<td>[-1,1,1]<td>-1/3,1/3,1/3<td>5/12,2/3,0
</tr>
<tr>
<td><tt>-z+1/2,-y+1,-x+1/2</tt>
<td>2<td>[-1,0,1]<td>0,0,0<td>1/2,1/2,0
</tr>
<tr>
<td><tt>-y+3/4,-z+3/4,x</tt>
<td>3^1<td>[1,-1,1]<td>0,0,0<td>0,3/4,0
</tr>
<tr>
<td><tt>z+3/4,-y+1/2,x+1/4</tt>
<td>2<td>[1,0,1]<td>1/2,0,1/2<td>1/4,1/4,0
</tr>
<tr>
<td><tt>-z+1,y+3/4,x+3/4</tt>
<td>4^-1<td>[0,1,0]<td>0,3/4,0<td>1/8,0,7/8
</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+1/4,-z-1/4</tt>
<td>-4^1<td>[0,0,1]<td>0,0,0<td>3/8,-1/8,-1/8
</tr>
<tr>
<td><tt>x-1/4,y+1/4,-z-1/2</tt>
<td>-2<td>[0,0,1]<td>-1/4,1/4,0<td>0,0,-1/4
</tr>
<tr>
<td><tt>-y-1/4,x+1/2,-z-3/4</tt>
<td>-4^-1<td>[0,0,1]<td>0,0,0<td>-3/8,1/8,-3/8
</tr>
<tr>
<td><tt>-x+1/2,y+1/4,z-1/4</tt>
<td>-2<td>[1,0,0]<td>0,1/4,-1/4<td>1/4,0,0
</tr>
<tr>
<td><tt>-y-1/4,-x+1/4,z-1/2</tt>
<td>-2<td>[1,1,0]<td>-1/4,1/4,-1/2<td>0,0,0
</tr>
<tr>
<td><tt>x-1/4,-y+1/2,z-3/4</tt>
<td>-2<td>[0,1,0]<td>-1/4,0,-3/4<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+1/4,-y-1/4</tt>
<td>-2<td>[0,1,1]<td>1/2,1/4,-1/4<td>0,0,0
</tr>
<tr>
<td><tt>z-1/4,x+1/4,-y-1/2</tt>
<td>-3^-1<td>[-1,1,1]<td>0,0,0<td>-1/2,-1/4,-1/4
</tr>
<tr>
<td><tt>-x-1/4,z+1/2,-y-3/4</tt>
<td>-4^1<td>[1,0,0]<td>0,0,0<td>-1/8,-1/8,-5/8
</tr>
<tr>
<td><tt>-z+1/2,x+1/4,y-1/4</tt>
<td>-3^-1<td>[1,-1,1]<td>0,0,0<td>1/4,1/2,1/4
</tr>
<tr>
<td><tt>-x-1/4,-z+1/4,y-1/2</tt>
<td>-4^-1<td>[1,0,0]<td>0,0,0<td>-1/8,3/8,-1/8
</tr>
<tr>
<td><tt>z-1/4,-x+1/2,y-3/4</tt>
<td>-3^1<td>[-1,-1,1]<td>0,0,0<td>-1/4,3/4,0
</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,z-1/4,x-1/4</tt>
<td>-3^-1<td>[-1,-1,1]<td>0,0,0<td>1/4,-1/4,0
</tr>
<tr>
<td><tt>-z+1/4,-y-1/4,x-1/2</tt>
<td>-4^1<td>[0,1,0]<td>0,0,0<td>3/8,-1/8,-1/8
</tr>
<tr>
<td><tt>y+1/4,-z,x-3/4</tt>
<td>-3^1<td>[-1,1,1]<td>0,0,0<td>1/2,1/4,-1/4
</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+1/4,z+1/4,-x</tt>
<td>-3^1<td>[1,-1,1]<td>0,0,0<td>1/4,0,-1/4
</tr>
<tr>
<td><tt>-z+1/4,y+1/2,-x-1/4</tt>
<td>-2<td>[1,0,1]<td>1/4,1/2,-1/4<td>0,0,0
</tr>
<tr>
<td><tt>z,-y+1/4,-x-3/4</tt>
<td>-4^-1<td>[0,1,0]<td>0,0,0<td>-3/8,1/8,-3/8
</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>i<td>192<td>1<td><tt>x,y,z</tt>
</tr>
<tr>
<td>h<td>96<td>2<td><tt>0,y,-y</tt>
</tr>
<tr>
<td>g<td>96<td>m<td><tt>x,x,z</tt>
</tr>
<tr>
<td>f<td>48<td>mm2<td><tt>x,1/8,1/8</tt>
</tr>
<tr>
<td>e<td>32<td>3m<td><tt>x,x,x</tt>
</tr>
<tr>
<td>d<td>16<td>-3m<td><tt>1/2,1/2,1/2</tt>
</tr>
<tr>
<td>c<td>16<td>-3m<td><tt>0,0,0</tt>
</tr>
<tr>
<td>b<td>8<td>-43m<td><tt>3/8,3/8,3/8</tt>
</tr>
<tr>
<td>a<td>8<td>-43m<td><tt>1/8,1/8,1/8</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+1/4,1/4</tt><td>[0,0,1]<td>0,1/4,1/4
</tr>
<tr>
<td><tt>2*x+3/4,2*y+1/4,1/2</tt><td>[0,0,1]<td>3/4,1/4,1/2
</tr>
<tr>
<td><tt>0,2*y+1/4,2*z+1/4</tt><td>[1,0,0]<td>0,1/4,1/4
</tr>
<tr>
<td><tt>x+y+3/4,-x-y+1/4,2*z+1/2</tt><td>[1,1,0]<td>3/4,1/4,1/2
</tr>
<tr>
<td><tt>2*x+3/4,0,2*z+3/4</tt><td>[0,1,0]<td>3/4,0,3/4
</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+1/4,-y-z+1/4</tt><td>[0,1,1]<td>0,1/4,1/4
</tr>
<tr>
<td><tt>3/4,y-z,-y-z+3/4</tt><td>[1,0,0]<td>3/4,0,3/4
</tr>
<tr>
<td><tt>x+z+3/4,-x-y,-y+z+3/4</tt><td>[-1,-1,1]<td>3/4,0,3/4
</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+1/4,3/4,x+z+1/2</tt><td>[0,1,0]<td>1/4,3/4,1/2
</tr>
<tr>
<td><tt>x+y+1/4,y-z+1/2,x+z+3/4</tt><td>[-1,1,1]<td>1/4,1/2,3/4
</tr>
<tr>
<td><tt>x+z,2*y+1/2,x+z+1/2</tt><td>[-1,0,1]<td>0,1/2,1/2
</tr>
<tr>
<td><tt>x+y+1/4,y-z+1/4,-x-z</tt><td>[1,-1,1]<td>1/4,1/4,0
</tr>
<tr>
<td><tt>x+z+1/4,2*y,-x-z+1/4</tt><td>[1,0,1]<td>1/4,0,1/4
</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: (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.

</pre>
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