Mathematical Notes

, Volume 95, Issue 5–6, pp 795–805 | Cite as

Interior Klein polyhedra

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Abstract

The convex hull of all integer points of a noncompact polyhedron is closed and is a generalized polyhedron only under certain conditions. It is proved that if only the integer points in the interior of the polyhedron are taken, then most of the conditions can be dropped. Moreover, the object thus obtained has properties resembling those of a Klein polyhedron, and it is a Klein polyhedron in the case of an irrational simplicial cone.

Keywords

continued fraction Klein polyhedron interior Klein polyhedron simplicial cone 

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© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.National Research University Higher School of EconomicsMoscowRussia
  2. 2.Moscow State UniversityMoscowRussia

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