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Self-intersecting polytopes in any dimension are called star polytopes.

How is a polytope being self-intersecting defined? Thanks!

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Depends on your definition of a polytope. If it's some collection of faces (edges, vertices, ...) then it will be self-intersecting if there is some pair of faces that intersect each other non-trivially (meaning they just don't share a common subface of the polytope). – Marek Dec 15 '12 at 23:39

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