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.”
Recommended Citation
Damian, Mirela; Demaine, Erik; Flatland, Robin; and O'Rourke, Joseph, "Unfolding Genus-2 Orthogonal Polyhedra with Linear Refinement" (2016). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/28
Comments
Peer reviewed accepted manuscript.