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Proceedings of the Steklov Institute of Mathematics

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

Properties of faces of parallelohedra

  • N. P. Dolbilin
Article

Abstract

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.

Keywords

STEKLOV Institute Convex Polytope Nonempty Intersection Hexagonal Prism Standard Face 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  1. 1.Steklov Institute of MathematicsRussian Academy of SciencesMoscowRussia

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