Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 50, No. 1, pp. 71-79 (2009)

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The lonely vertex problem

D. Frettlöh and A. Glazyrin

Fakultät für Mathematik, Universität Bielefeld, Bielefeld, Germany, e-mail:; Moscow State University, Leninskie Gory, 119992 Moscow GSP-2, Russia, e-mail:

Abstract: In a locally finite tiling of $\R^n$ by convex polytopes, each point $x \in \R^n$ is either a vertex of at least two tiles, or no vertex at all.

Keywords: tilings, convex polytopes

Classification (MSC2000): 52C22, 52C07

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Electronic version published on: 29 Dec 2008. This page was last modified: 28 Jan 2013.

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