3-TRIANGULATIONS OF POLYHEDRA AND THEIR CONNECTION GRAPHS
Milica Stojanović · Facta Universitatis Series Mathematics and Informatics · 2024
Here we investigate the properties of 3-triangulation of polyhedra, whenpossible. Namely, it is known that 3-triangulation of convex polyhedra is always possible, but this is not the case with all non-convex ones. This is the reason to consider the decomposition of non-convex polyhedra into convex pieces if possible. After that, we introduce the connection graph for the 3-triangulable polyhedron in such a way that these pieces are represented by the nodes of the graph. First, our attention shall be focused on toroids, a special class of non-convex polyhedra, and the minimal number of tetrahedra necessary to 3-triangulate them. As another application of connection graphs, we shall also consider those corresponding to convex polyhedra, especially to conic triangulation of them.