Classifying simplicial dissections of convex polyhedra with symmetry

Abstract

A convex polyhedron is the convex hull of a finite set ofpoints in R3. A triangulation of a convex polyhedron is a decomposition into a finite number of 3-simplices such that any two intersect in a common face or are disjoint. A simplicial dissection is a decomposition into a finite number of 3-simplices such that no two share an interior point. We present an algorithm to classify the simplicial dissections of a regular polyhedron under the symmetry group of the polyhedron.