  In 1929 B.~N.~Delaunay proved that there are exactly 5 types of coincidence
of parallelohedra at faces of codimension 3. We give a combinatorial proof of
this theorem and prove several additional statements on three-codimensional
faces of parallelohedral tiling.
  --
  The original paper appeared in 2013 in MAIS (see the bibref) and was in
Russian. This is the English version.
