Convex polyhedra with triangular faces and cone triangulation

Considering the problem of the minimal triangulation for a given polyhedra (dividing polyhedra into tetrahedra) it is known that the cone triangulation provides the number of tetrahedra which is the smallest, or the closest to it. It is also shown that when we want to know whether the cone triangulation is the minimal one, it is necessary to find the order of all vertices, as well as the order of 'separating circles'. Here, we will give algorithms for testing the necessary condition for the cone triangulation if it is the minimal one. The algorithm for forming the cone triangulation will also be given.