[<a href="http://cci.lbl.gov:443/cctbx/">Index of services</a>]
[<a href="http://cci.lbl.gov:443/cctbx/explore_symmetry.html">New input</a>]
<hr>
<pre>
Input space group symbol: C 4ac -1ac
Convention: Hall symbol

Number of lattice translations: 2
Space group is centric.
Number of representative symmetry operations: 4
Total number of symmetry operations: 16

Parallelepiped containing an asymmetric unit:
  cctbx Error: Brick is not available for the given space group representation.

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+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+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,-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+1/2,-y,-z+1/2</tt>
<td>-1<td>-<td>-<td>1/4,0,1/4
</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-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+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>1<td>-<td>-<td>-
</tr>
<tr>
<td><tt>-y+1,x+1/2,z+1/2</tt>
<td>4^1<td>[0,0,1]<td>0,0,1/2<td>1/4,3/4,0
</tr>
<tr>
<td><tt>-x+1,-y+1,z</tt>
<td>2<td>[0,0,1]<td>0,0,0<td>1/2,1/2,0
</tr>
<tr>
<td><tt>y+1/2,-x+1,z+1/2</tt>
<td>4^-1<td>[0,0,1]<td>0,0,1/2<td>3/4,1/4,0
</tr>
<tr>
<td><tt>-x+1,-y+1/2,-z+1/2</tt>
<td>-1<td>-<td>-<td>1/2,1/4,1/4
</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,-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,x,-z</tt>
<td>-4^-1<td>[0,0,1]<td>0,0,0<td>1/2,1/2,0
</tr>
</table><pre>

Space group number: 86
Conventional Hermann-Mauguin symbol: P 42/n :2
Universal    Hermann-Mauguin symbol: P 42/n :2 (a+b-1/4,-a+b-1/4,c-1/4)
Hall symbol: -P 4bc (1/2*x+1/2*y+1/4,-1/2*x+1/2*y,z+1/4)
Change-of-basis matrix: x-y-1/4,x+y-1/4,z-1/4
               Inverse: 1/2*x+1/2*y+1/4,-1/2*x+1/2*y,z+1/4

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>g<td>16<td>1<td><tt>x,y,z</tt>
</tr>
<tr>
<td>f<td>8<td>2<td><tt>1/2,0,z</tt>
</tr>
<tr>
<td>e<td>8<td>2<td><tt>1/4,1/4,z</tt>
</tr>
<tr>
<td>d<td>8<td>-1<td><tt>1/4,0,3/4</tt>
</tr>
<tr>
<td>c<td>8<td>-1<td><tt>1/4,0,1/4</tt>
</tr>
<tr>
<td>b<td>4<td>-4<td><tt>1/2,0,0</tt>
</tr>
<tr>
<td>a<td>4<td>-4<td><tt>1/2,0,1/2</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+1/2,-x-y,1/2</tt><td>[0,0,1]<td>1/2,0,1/2
</tr>
<tr>
<td><tt>2*x+1/2,2*y+1/2,0</tt><td>[0,0,1]<td>1/2,1/2,0
</tr>
</table><pre>

Additional generators of Euclidean normalizer:
  Number of structure-seminvariant vectors and moduli: 2
    Vector    Modulus
    (1, 0, 0) 2
    (0, 0, 1) 2
  Further generators:
</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>-2<td>[0,1,0]<td>0,0,0<td>0,0,0
</tr>
</table><pre>

Grid factors implied by symmetries:
  Space group: (2, 2, 2)
  Structure-seminvariant vectors and moduli: (2, 1, 2)
  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>
<hr>
[<a href="http://cci.lbl.gov:443/cctbx/">Index of services</a>]
[<a href="http://cci.lbl.gov:443/cctbx/explore_symmetry.html">New input</a>]