Proceedings of the Steklov Institute of Mathematics

, Volume 266, Issue 1, pp 105–119 | Cite as

Properties of faces of parallelohedra

  • N. P. Dolbilin


We consider an important class of polytopes, called parallelohedra, that tile the Euclidean space. The concepts of a standard face of a parallelohedron and of the index of a face are introduced. It is shown that the sum of indices of standard faces in a parallelohedron is an invariant; this implies the Minkowski bound for the number of facets of parallelohedra. New properties of faces of parallelohedra are obtained.


STEKLOV Institute Convex Polytope Nonempty Intersection Hexagonal Prism Standard Face 
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© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  1. 1.Steklov Institute of MathematicsRussian Academy of SciencesMoscowRussia

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