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Main Title: Vertex-facet incidences of unbounded polyhedra
Author(s): Joswig, Michael
Kaibel, Volker
Pfetsch, Marc E.
Ziegler, Günter M.
Type: Article
Language Code: en
Abstract: How much of the combinatorial structure of a pointed polyhedron is contained in its vertex-facet incidences? Not too much, in general, as we demonstrate by examples. However, one can tell from the incidence data whether the polyhedron is bounded. In the case of a polyhedron that is simple and ``simplicial,'' i.e., a d-dimensional polyhedron that has d facets through each vertex and d vertices on each facet, we derive from the structure of the vertexfacet incidence matrix that the polyhedron is necessarily bounded. In particular, this yields a characterization of those polyhedra that have circulants as vertex-facet incidence matrices.
Issue Date: 2001
Date Available: 2-Oct-2018
DDC Class: 510 Mathematik
Subject(s): combinatorial structure
incidence matrix
Journal Title: Advances in Geometry
Publisher: De Gruyter
Publisher Place: Berlin
Volume: 1
Issue: 1
Publisher DOI: 10.1515/advg.2001.002
Page Start: 23
Page End: 36
EISSN: 1615-7168
ISSN: 1615-715X
Notes: Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.
This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.
Appears in Collections:Inst. Mathematik » Publications

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