Paper by Erik D. Demaine

Mirela Damian, Erik D. Demaine, Robin Flatland, and Joseph O'Rourke, “Unfolding Genus-2 Orthogonal Polyhedra with Linear Refinement”, Graphs and Combinatorics, volume 33, number 5, 2017, pages 1357–1379.

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.

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Related papers:
DeltaUnfolding_GC (Unfolding Orthogonal Polyhedra with Quadratic Refinement: The Delta-Unfolding Algorithm)

See also other papers by Erik Demaine.
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Last updated March 12, 2024 by Erik Demaine.