Unfolding some classes of orthogonal polyhedra of arbitrary genus

Kuan-Yi Ho (), Yi-Jun Chang () and Hsu-Chun Yen ()
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Kuan-Yi Ho: National Taiwan University
Yi-Jun Chang: University of Michigan
Hsu-Chun Yen: National Taiwan University

Journal of Combinatorial Optimization, 2019, vol. 37, issue 2, No 6, 482-500

Abstract: Abstract Unfolding polyhedra beyond genus zero (i.e., with holes) is challenging, yet it has not been investigated until very recently. We show two types of orthogonal polyhedra of arbitrary genus, namely, well-separated orthographs and regular orthogonal polyhedra with x- and z-holes, to enjoy $$(2 \times 1)$$ ( 2 × 1 ) -grid-unfoldings, generalizing some prior works. In addition to the development of new unfolding techniques, for the first time we identify classes of nontrivial orthogonal polyhedra of arbitrary genus to admit grid-unfoldings subject to a small amount of refinements.

Keywords: Genus; Orthogonal polyhedra; Orthograph; Unfolding (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10878-018-0299-1

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