Vertex-Facet Incidences of Unbounded Polyhedra

Details Vertex-Facet Incidences of Unbounded Polyhedra Vertex-Facet Incidences of Unbounded Polyhedra

2000-06-29

arxiv.org/abs/math/0006225v1

Mathematics

Combinatorics

LaTeX2e, 14 pages with 4 figures

Scientific paper

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 vertex-facet 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.

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