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arXiv · 1611.00106

Unfolding Genus-2 Orthogonal Polyhedra with Linear Refinement

Mirela Damian·Erik Demaine·Robin Flatland·Joseph O'Rourke
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Abstract

We show that every orthogonal polyhedron of genus at most 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.

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Mirela Damian, Erik Demaine, Robin Flatland, Joseph O'Rourke. 2016-11-01. Unfolding Genus-2 Orthogonal Polyhedra with Linear Refinement. https://arxiv.org/abs/1611.00106

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