Unfolding Genus-2 Orthogonal Polyhedra with Linear Refinement
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Author(s)
Damian, Mirela
Flatland, Robin
O’Rourke, Joseph
Demaine, Erik D
Date Issued
September 2017
Journal
Graphs and Combinatorics
Publisher
Springer Japan
Citation
Damian, Mirela, et al. “Unfolding Genus-2 Orthogonal Polyhedra with Linear Refinement.” Graphs and Combinatorics, vol. 33, no. 5, Sept. 2017, pp. 1357–79.
Version
Author's final manuscript
Abstract
We show that every orthogonal polyhedron of genus g≤2 can be unfolded without overlap while using only a linear number of orthogonal cuts (parallel to the polyhedron edges). This is the first result on unfolding general orthogonal polyhedra beyond genus-0. Our unfolding algorithm relies on the existence of at most 2 special leaves in what we call the “unfolding tree” (which ties back to the genus), so unfolding polyhedra of genus 3 and beyond requires new techniques. Keywords: Grid unfolding, Linear refinement, Orthogonal polyhedron, Genus 2
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s00373-017-1849-5
