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<pre>
Result of symbol lookup:
  Space group number: 91
  Schoenflies symbol: D4^3
  Hermann-Mauguin symbol: P 41 2 2
  Hall symbol: P 4w 2c

Input space group symbol: P 41 2 2
Convention: Default

Number of lattice translations: 1
Space group is acentric.
Space group is chiral.
Space group is enantiomorphic.
Number of representative symmetry operations: 8
Total number of symmetry operations: 8

Parallelepiped containing an asymmetric unit:
  0&lt;=x&lt;=1/2; 0&lt;=y&lt;=1/2; -1/8&lt;=z&lt;=3/8

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+1/4</tt>
<td>4^1<td>[0,0,1]<td>0,0,1/4<td>0,0,0
</tr>
<tr>
<td><tt>-x,-y,z+1/2</tt>
<td>2<td>[0,0,1]<td>0,0,1/2<td>0,0,0
</tr>
<tr>
<td><tt>y,-x,z+3/4</tt>
<td>4^-1<td>[0,0,1]<td>0,0,3/4<td>0,0,0
</tr>
<tr>
<td><tt>x,-y,-z+1/2</tt>
<td>2<td>[1,0,0]<td>0,0,0<td>0,0,1/4
</tr>
<tr>
<td><tt>y,x,-z+3/4</tt>
<td>2<td>[1,1,0]<td>0,0,0<td>0,0,3/8
</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+1/4</tt>
<td>2<td>[-1,1,0]<td>0,0,0<td>0,0,1/8
</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>d<td>8<td>1<td><tt>x,y,z</tt>
</tr>
<tr>
<td>c<td>4<td>2<td><tt>x,x,3/8</tt>
</tr>
<tr>
<td>b<td>4<td>2<td><tt>1/2,y,0</tt>
</tr>
<tr>
<td>a<td>4<td>2<td><tt>0,y,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,1/4</tt><td>[0,0,1]<td>0,0,1/4
</tr>
<tr>
<td><tt>2*x,2*y,1/2</tt><td>[0,0,1]<td>0,0,1/2
</tr>
<tr>
<td><tt>0,2*y,2*z+1/2</tt><td>[1,0,0]<td>0,0,1/2
</tr>
<tr>
<td><tt>x+y,-x-y,2*z+3/4</tt><td>[1,1,0]<td>0,0,3/4
</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+1/4</tt><td>[-1,1,0]<td>0,0,1/4
</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

Grid factors implied by symmetries:
  Space group: (1, 1, 4)
  Structure-seminvariant vectors and moduli: (2, 2, 2)
  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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