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Vertex-facet incidences of unbounded polyhedra

Joswig, Michael; Kaibel, Volker; Pfetsch, Marc E.; Ziegler, Günter M.

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.
Published in: Advances in Geometry, 10.1515/advg.2001.002, De Gruyter
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