Unfolding Genus-2 Orthogonal Polyhedra with Linear Refinement
Author(s)Damian, Mirela; Flatland, Robin; O’Rourke, Joseph; Demaine, Erik D
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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
DepartmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Graphs and Combinatorics
Damian, Mirela, et al. “Unfolding Genus-2 Orthogonal Polyhedra with Linear Refinement.” Graphs and Combinatorics, vol. 33, no. 5, Sept. 2017, pp. 1357–79.
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