Unfolding Prismatoids as Convex Patches: Counterexamples and Positive Results

9 May 2012Joseph O'Rourke

We address the unsolved problem of unfolding prismatoids in a new context, viewing a "topless prismatoid" as a convex patch---a polyhedral subset of the surface of a convex polyhedron homeomorphic to a disk. We show that several natural strategies for unfolding a prismatoid can fail, but obtain a positive result for "petal unfolding" topless prismatoids... (read more)

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