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.Comment: LaTeX2e, 14 pages with 4 figure
