Unfolding Genus-2 Orthogonal Polyhedra with Linear Refinement

Authors

Mirela Damian, Villanova University
Erik Demaine, Massachusetts Institute of Technology
Robin Flatland, Siena College
Joseph O'Rourke, Smith CollegeFollow

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.”

Comments

Peer reviewed accepted manuscript.

Recommended Citation

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