Algorithms for investigating optimality of cone triangulation for a polyhedron

Abstract

The problem of finding minimal triangulation of a given polyhedra (dividing polyhedra into tetrahedra) is very actual now. It is known that cone triangulation for a polyhedron provides the smallest number of tetrahedra, or close to it. In earlier investigations when this triangulation was the optimal one, it was shown that conditions for vertices to be of the order five, six or for separated vertices of order four was only the necessary ones. It was shown that then if it exists the "separating circle" of order less then six, for two vertices of order six, cone triangulation is not the minimal one. Here, test algorithms will be given, for the case when the given polyhedron has separating circle of order five or less.