Neighborly 4-Polytopes and Neighborly Combinatorial 3-Manifolds with Ten Vertices

Abstract

A combinatorial n-sphere is a simplicial n-complex whose body (i.e., the union of its members) is homeomorphic to the topological n-sphere Sn. A combinatorial n-manifold is a simplicial n-complex M such that M is connected, and for every vertex x in M the complex linker, M), the link of x in M, is a combinatorial (n — 1)-sphere. For more details the reader should consult Alexander [1] and Grünbaum [16]. All the spheres and manifolds to which we refer are combinatorial.