d4 Szilassi Polyhedron

Thanks to Ed Pegg for suggesting this concept

This shape may only be printable in Frosted Ultra Detail due to its thin edges. Printing in other materials may fail.

The Szilassi Polyhedron is a nonconvex toroidal polyhedron with seven hexagonal faces in which each face shares an edge with each other face. The tetrahedron and the Szilassi polyhedron are the only two known polyhedra in which each face shares an edge with each other face. Like the tetrahedron, the Szilassi polyhedron can be used as a d4 since it can only land in four positions. For fun, this has been labelled "1" through "7", however it is usable as a d4 since it can only produce "1" through "4" as results.

This has been posted to Shapeways as a curio and I cannot guarantee that it will act properly as a d4 die or that it will even print successfully.