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We give a concise definition of mitered offset surfaces for nonconvex polytopes in     R   3   , along with a proof of existence and a discussion of basic properties. These results imply the existence of 3D straight skeletons for general nonconvex polytopes. The geometric, topological, and algorithmic features of such skeletons are investigated, including a classification of their constructing events in the generic case. Our results extend to the weighted setting, to a larger class of polytope decompositions, and to general dimensions. For (weighted) straight skeletons of an n -facet polytope in     R   d   , an upper bound of    O  (   n  d   )   on their combinatorial complexity is derived. It relies on a novel layer partition for straight skeletons, and improves the trivial bound by an order of magnitude for    d  ≥  3   .

Straight Skeletons and Mitered Offsets of Nonconvex Polytopes