无界多面体的点-面关联
Vertex-Facet Incidences of Unbounded Polyhedra
摘要：
一个尖多面体的顶点与小平面的关联包含了多少组合结构？一般来说，不太多，正如我们通过例子所证明的那样。然而，人们可以从关联数据判断多面体是否有界。在多面体是简单的和“单纯的”的情况下，即，一个d维多面体，它有d个面通过每个顶点，在每个面上有d个顶点，我们从顶点-面关联矩阵的结构中得出该多面体必然是有界的。特别地，这产生了具有作为顶点-小平面关联矩阵的循环的那些多面体的表征。
英文摘要：
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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