Document Type

Article

Publication Date

11-2016

Publication Title

Graphs and Combinatorics

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

DOI

10.1007/s00373-017-1849-5

Rights

“Licensed to Smith College and distributed CC-BY under the Smith College Faculty Open Access Policy.”

Included in

Mathematics Commons

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