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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!

Crosspost: https://mathoverflow.net/questions/53601/which-platonic-solids-can-form-a-topological-torus

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MathWorld (about half-way down the page) says it can be done with 8, but does not say that's a minimum.

diagram of 8 dodecahedrons arranged in a ring

(diagram from MathWorld page)

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