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<pre>
Result of symbol lookup:
  Space group number: 81
  Schoenflies symbol: S4^1
  Hermann-Mauguin symbol: P -4
  Hall symbol: P -4

Input space group symbol: P -4
Convention: Default

Number of lattice translations: 1
Space group is acentric.
Number of representative symmetry operations: 4
Total number of symmetry operations: 4

Parallelepiped containing an asymmetric unit:
  0&lt;=x&lt;=1/2; 0&lt;=y&lt;=1/2; 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,-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>
</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>h<td>4<td>1<td><tt>x,y,z</tt>
</tr>
<tr>
<td>g<td>2<td>2<td><tt>0,1/2,z</tt>
</tr>
<tr>
<td>f<td>2<td>2<td><tt>1/2,1/2,z</tt>
</tr>
<tr>
<td>e<td>2<td>2<td><tt>0,0,z</tt>
</tr>
<tr>
<td>d<td>1<td>-4<td><tt>1/2,1/2,1/2</tt>
</tr>
<tr>
<td>c<td>1<td>-4<td><tt>1/2,1/2,0</tt>
</tr>
<tr>
<td>b<td>1<td>-4<td><tt>0,0,1/2</tt>
</tr>
<tr>
<td>a<td>1<td>-4<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>2*x,2*y,0</tt><td>[0,0,1]<td>0,0,0
</tr>
</table><pre>

Additional generators of Euclidean normalizer:
  Number of structure-seminvariant vectors and moduli: 2
    Vector    Modulus
    (0, 0, 1) 2
    (1, 1, 0) 2
  Inversion through a centre at: 0,0,0
  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>y,x,z</tt>
<td>-2<td>[-1,1,0]<td>0,0,0<td>0,0,0
</tr>
</table><pre>

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