This article is cited in 2 papers

Interior Klein Polyhedra

I. A. Makarov<sup>ab

a</sup> M. V. Lomonosov Moscow State University
^b National Research University "Higher School of Economics", Moscow

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.

UDC: 511.9

Received: 01.11.2012
Revised: 03.10.2013

DOI: 10.4213/mzm9340

 English version: Mathematical Notes, 2014, 95:6, 795–805

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