Nonconvex embeddings of the exceptional simplicial 3-spheres with 8 vertices

摘要

As shown by D. Barnette (1973, J. Combin. Theory Ser. A 14, 37 53) there are precisely 39 simplicial 3-spheres with 8 vertices. Thirty-seven of these are boundary complexes for convex 4-polytopes. In this paper we supply nonconvex embeddings in Euclidean 4-space for the remaining two 3-spheres, We discuss the properties of the embeddings as well as the techniques used to demonstrate their validity. (C) 2002 Elsevier Science (USA). [References: 21]