Four Kinds of Twins
1. Twinning by merohedry  
Twin operator: symmetry operator of the crystal system but not of the point group of the crystal

1.1. racemic twin

1.2. twin operator: not of the Laue group of the crystal

possible in tetragonal, trigonal, hexagonal or cubic crystal systems

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 2. Twinning by pseudo-merohedry
  twin operator: belongs to a higher crystal system than the structure  
possible if the metric symmetry is higher than the symmetry of the structure  
e.g. monoclinic structure with ß = 90°

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 3. Twinning by reticular merohedry
  e.g. obverse/reverse twinning in case of a rhombohedral crystal  
systematic absent reflections for one domain are present for the others and vice versa

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4. Non-merohedral twins
 

twin operator : arbitrary operator