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<pre>
Result of symbol lookup:
  Space group number: 80
  Schoenflies symbol: C4^6
  Hermann-Mauguin symbol: I 41
  Hall symbol: I 4bw

Input space group symbol: I 41
Convention: Default

Number of lattice translations: 2
Space group is acentric.
Space group is chiral.
Number of representative symmetry operations: 4
Total number of symmetry operations: 8

Parallelepiped containing an asymmetric unit:
  0&lt;=x&lt;=1/4; 1/4&lt;=y&lt;=3/4; 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+1/2,z+1/4</tt>
<td>4^1<td>[0,0,1]<td>0,0,1/4<td>-1/4,1/4,0
</tr>
<tr>
<td><tt>-x+1/2,-y+1/2,z+1/2</tt>
<td>2<td>[0,0,1]<td>0,0,1/2<td>1/4,1/4,0
</tr>
<tr>
<td><tt>y+1/2,-x,z+3/4</tt>
<td>4^-1<td>[0,0,1]<td>0,0,3/4<td>1/4,-1/4,0
</tr>
<tr>
<td><tt>x+1/2,y+1/2,z+1/2</tt>
<td>1<td>-<td>-<td>-
</tr>
<tr>
<td><tt>-y+1/2,x+1,z+3/4</tt>
<td>4^1<td>[0,0,1]<td>0,0,3/4<td>-1/4,3/4,0
</tr>
<tr>
<td><tt>-x+1,-y+1,z+1</tt>
<td>2<td>[0,0,1]<td>0,0,1<td>1/2,1/2,0
</tr>
<tr>
<td><tt>y+1,-x+1/2,z+5/4</tt>
<td>4^-1<td>[0,0,1]<td>0,0,5/4<td>3/4,-1/4,0
</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>b<td>8<td>1<td><tt>x,y,z</tt>
</tr>
<tr>
<td>a<td>4<td>2<td><tt>0,0,z</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+1/2,1/4</tt><td>[0,0,1]<td>0,1/2,1/4
</tr>
<tr>
<td><tt>2*x+1/2,2*y+1/2,1/2</tt><td>[0,0,1]<td>1/2,1/2,1/2
</tr>
</table><pre>

Additional generators of Euclidean normalizer:
  Number of structure-seminvariant vectors and moduli: 1
    Vector    Modulus
    (0, 0, 1) 0
  Inversion through a centre at: 1/4,0,0
  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: (2, 2, 4)
  Structure-seminvariant vectors and moduli: (1, 1, 1)
  Euclidean normalizer: (2, 2, 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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