Extremal properties for dissections of convex 3-polytopes

A dissection of a convex d-polytope is a partition of the polytope into d-s implices whose vertices are among the vertices of the polytope. Triangulati ons are dissections that have the additional property that the set of all i ts simplices forms a simplicial complex. The size of a dissection is the nu mber of d-simplices it contains. This paper compares triangulations of maxi mal size with dissections of maximal size. We also exhibit lower and upper bounds for the size of dissections of a 3-polytope and analyze extremal siz e triangulations for specific nonsimplicial polytopes: prisms, antiprisms, Archimedean solids, and combinatorial d-cubes.