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Unfolding some classes of orthogonal polyhedra of arbitrary genus

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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 \((2 \times 1)\)-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.

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Acknowledgements

The authors thank the anonymous referee for comments that improved the presentation of this paper.

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Authors and Affiliations

  1. National Taiwan University, Taipei, Taiwan

    Kuan-Yi Ho & Hsu-Chun Yen

  2. University of Michigan, Ann Arbor, MI, USA

    Yi-Jun Chang

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  1. Kuan-Yi Ho
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  2. Yi-Jun Chang
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  3. Hsu-Chun Yen
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Corresponding author

Correspondence to Hsu-Chun Yen.

Additional information

A preliminary version of this paper was presented at the 23rd International Computing and Combinatorics Conference (COCOON’17) during August 3–5, 2017, in Hong Kong, China

Research supported in part by MOST-106-2221-E-002-036-MY3.

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Ho, KY., Chang, YJ. & Yen, HC. Unfolding some classes of orthogonal polyhedra of arbitrary genus. J Comb Optim 37, 482–500 (2019). https://doi.org/10.1007/s10878-018-0299-1

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  • DOI: https://doi.org/10.1007/s10878-018-0299-1

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