3-Sphären mit kleinen Eckenvalenzen. (3-spheres with small valences of the vertices) (Q1107828)

A (simplicial) (d-1)-sphere is called polytopal if it is isomorphic to the boundary complex of a convex d-polytope. A well-known theorem of Steinitz says that any 2-sphere is polytopal. The authors give - without proof - an interesting result showing that any 3-sphere is polytopal provided the valences of its vertices are small. The assumptions of this result cannot be weakened, as can be shown by means of examples. Some remarks on the proof are made and open problems are stated.