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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!


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up vote 3 down vote accepted

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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