Cosmic crystallography: the euclidean isometries
  Exact expressions for probability densities of conjugate pair separation in euclidean isometries are obtained, for the cosmic crystallography.These are the theoretical counterparts of the mean histograms arising from computer simulation of the isometries. For completeness, also the isometries with fixed points are examined, as well as the orientation reversing isometries. 
A. Bernui, A.F.F. Teixeira