How to Cut out a Convex Polyhedron
نویسنده
چکیده
It is known that one can fold a convex polyhedron from a non-overlapping face unfolding, but the complexity of the algorithm in [MP] remains an open problem. In this paper we show that every convex polyhedron P ⊂ R can be obtained in polynomial time, by starting with a cube which contains P and sequentially cutting out the extra parts of the surface. Our main tool is of independent interest. We prove that given a convex polytope P in R and a facet F of P , then F is contained in the union ∪G 6=F AG. Here the union is over all the facets G of P different from F , and AG is the set obtained from G by rotating towards F the hyperplane spanned by G about the intersection of it with the hyperplane spanned by F .
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