I don't know if this will help. It's a diagram that I drew a few years ago (when teaching a geometry course) to illustrate how to triangulate a torus as a cube with a hole through the middle from top to bottom. It has 16 vertices, 32 edges and 16 quadrilateral faces. If you want triangular faces, you can divide each quadrilateral into two triangles by joining two opposite corners. That will double the number of faces, and also add 16 new edges.