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<pre>
Input space group symbol: C 4 2
Convention: Hall symbol

Number of lattice translations: 2
Space group is acentric.
Space group is chiral.
Number of representative symmetry operations: 8
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,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>
<tr>
<td><tt>x,-y,-z</tt>
<td>2<td>[1,0,0]<td>0,0,0<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>-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</tt>
<td>2<td>[-1,1,0]<td>0,0,0<td>0,0,0
</tr>
<tr>
<td><tt>x+1/2,y+1/2,z</tt>
<td>1<td>-<td>-<td>-
</tr>
<tr>
<td><tt>-y+1/2,x+1/2,z</tt>
<td>4^1<td>[0,0,1]<td>0,0,0<td>0,1/2,0
</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+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>2<td>[1,0,0]<td>1/2,0,0<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>-x+1/2,y+1/2,-z</tt>
<td>2<td>[0,1,0]<td>0,1/2,0<td>1/4,0,0
</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>
</table><pre>

Space group number: 89
Conventional Hermann-Mauguin symbol: P 4 2 2
Universal    Hermann-Mauguin symbol: P 4 2 2 (a+b,-a+b,c)
Hall symbol:  P 4 2 (1/2*x+1/2*y,-1/2*x+1/2*y,z)
Change-of-basis matrix: x-y,x+y,z
               Inverse: 1/2*x+1/2*y,-1/2*x+1/2*y,z

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>p<td>16<td>1<td><tt>x,y,z</tt>
</tr>
<tr>
<td>o<td>8<td>2<td><tt>x,-x+1/2,0</tt>
</tr>
<tr>
<td>n<td>8<td>2<td><tt>x,-x,1/2</tt>
</tr>
<tr>
<td>m<td>8<td>2<td><tt>x,-x+1/2,1/2</tt>
</tr>
<tr>
<td>l<td>8<td>2<td><tt>x,-x,0</tt>
</tr>
<tr>
<td>k<td>8<td>2<td><tt>x,0,1/2</tt>
</tr>
<tr>
<td>j<td>8<td>2<td><tt>x,0,0</tt>
</tr>
<tr>
<td>i<td>8<td>2<td><tt>1/4,1/4,z</tt>
</tr>
<tr>
<td>h<td>4<td>4<td><tt>1/2,0,z</tt>
</tr>
<tr>
<td>g<td>4<td>4<td><tt>0,0,z</tt>
</tr>
<tr>
<td>f<td>4<td>222<td><tt>1/4,-1/4,1/2</tt>
</tr>
<tr>
<td>e<td>4<td>222<td><tt>1/4,-1/4,0</tt>
</tr>
<tr>
<td>d<td>2<td>422<td><tt>1/2,0,1/2</tt>
</tr>
<tr>
<td>c<td>2<td>422<td><tt>1/2,0,0</tt>
</tr>
<tr>
<td>b<td>2<td>422<td><tt>0,0,1/2</tt>
</tr>
<tr>
<td>a<td>2<td>422<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>x-y,-x-y,0</tt><td>[0,0,1]<td>0,0,0
</tr>
<tr>
<td><tt>0,2*y,2*z</tt><td>[1,0,0]<td>0,0,0
</tr>
<tr>
<td><tt>x+y,-x-y,2*z</tt><td>[1,1,0]<td>0,0,0
</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</tt><td>[-1,1,0]<td>0,0,0
</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
  Inversion through a centre at: 0,0,0

Grid factors implied by symmetries:
  Space group: (2, 2, 1)
  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>
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