On 3-triangulation of toroids

Abstract

As toroid (polyhedral torus) could not be convex, it is questionable if it is possible to 3-triangulate them (i.e. divide into tetrahedra). Here, we will discuss some examples of toroids to show that for each $n \geq 7$, there exists a toroid for which triangulation is possible. Also we will study the neccessary number of tetrahedra for the minimal triangulation.