  A parallelohedron is called reducible, if it can be represented as a direct
product of two parallelohedra of lower dimension. In his Ph.D. thesis (2005)
the first author proved a criterion of reducibility of a parallelohedron in
terms of the Venkov graph. In December 2011 the second author presented a
slightly revised version of the original proof at the seminar "Discrete
Geometry and Geometry of Numbers" (Moscow State University). The present paper
follows that talk.
