math_groups_discgeom

Vertex-facet incidences of unbounded polyhedra

Michael Joswig and Volker Kaibel and Marc E. Pfetsch and Günter M. Ziegler— 2001

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.

TitelVertex-facet incidences of unbounded polyhedra
VerfasserMichael Joswig and Volker Kaibel and Marc E. Pfetsch and Günter M. Ziegler
Datum2001
Quelle/n
Erschienen inAdvances in Geometry, volume 1, pages 23-36
ArtText