Minimal simplicial dissections and triangulations of convex 3-polytopes
The authors prove here the following somewhat surprising results about convex 3-polytopes. Let \(P\) be such a polytope. First, it is possible that the minimum number of tetrahedra in a triangulation of \(P\) can be reduced if one permits interior vertices. Second, there may be dissections of \(P\) into tetrahedra which use fewer tetrahedra than any triangulation. Third, the number of tetrahedra in a minimal triangulation of \(P\) may depend on the geometrical realization of \(P\) (as a combinatorial type). The families of examples they produce exhibit increasing large discrepancies.
scientific article; zbMATH DE number 1495779