Puzzling the 120-cell
Geometric Topology
2015-11-23 v2 History and Overview
Abstract
We introduce Quintessence: a family of burr puzzles based on the geometry and combinatorics of the 120-cell. We discuss the regular polytopes, their symmetries, the dodecahedron as an important special case, the three-sphere, and the quaternions. We then construct the 120-cell, giving an illustrated survey of its geometry and combinatorics. This done, we describe the pieces out of which Quintessence is made. The design of our puzzle pieces uses a drawing technique of Leonardo da Vinci; the paper ends with a catalogue of new puzzles.
Cite
@article{arxiv.1310.3549,
title = {Puzzling the 120-cell},
author = {Saul Schleimer and Henry Segerman},
journal= {arXiv preprint arXiv:1310.3549},
year = {2015}
}
Comments
25 pages, many figures. Exposition and figures improved throughout. This is the long version of the shorter published version