8 cubes can form a torus by gluing them together face-to-face, with each cube sharing a face with each of two other cubes, by torus I just mean a closed loop with a hole. Is the same possible with the dodecahedron? What is the minimum number of dodecahedrons needed for this?
Edit: Is it possible with the tetrahedron and icosahedron ?
Given a polytope, is there a general way to decide if it is possible, and to determine the minimum number?
Any good programmers around to check tetrahedron case?
Looking for software to check for small N!