Unfolding Face-Neighborhood Convex Patches: Counterexamples and Positive Results
نویسنده
چکیده
We address unsolved problems of unfolding polyhedra in a new context, focusing on special convex patches—disklike polyhedral subsets of the surface of a convex polyhedron. One long-unsolved problem is edge-unfolding prismatoids. We show that several natural strategies for unfolding a prismatoid can fail, but obtain a positive result for “petal unfolding” topless prismatoids, which can be viewed as particular convex patches. We also show that the natural extension of an earlier result on face-neighborhood convex patches fails, but we obtain a positive result for nonobtusely triangulated faceneighborhoods.
منابع مشابه
Unfolding Prismatoids as Convex Patches: Counterexamples and Positive Results
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. We also show that the natural extension to...
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