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Unfolding some classes of orthogonal polyhedra of arbitrary genus

Author

Listed:
  • Kuan-Yi Ho

    (National Taiwan University)

  • Yi-Jun Chang

    (University of Michigan)

  • Hsu-Chun Yen

    (National Taiwan University)

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.

Suggested Citation

  • Kuan-Yi Ho & Yi-Jun Chang & Hsu-Chun Yen, 2019. "Unfolding some classes of orthogonal polyhedra of arbitrary genus," Journal of Combinatorial Optimization, Springer, vol. 37(2), pages 482-500, February.
    • Handle: RePEc:spr:jcomop:v:37:y:2019:i:2:d:10.1007_s10878-018-0299-1
    DOI: 10.1007/s10878-018-0299-1
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