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A criterion of reducibility for a parallelohedron

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.

preprint2013arXivOpen access
Andrei OrdineAlexander Magazinov
math.MG
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Andrei OrdineAlexander Magazinov

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