Hypercube Unfoldings that Tile R^3 and R^2
Computational Geometry
2015-12-09 v2
Abstract
We show that the hypercube has a face-unfolding that tiles space, and that unfolding has an edge-unfolding that tiles the plane. So the hypercube is a "dimension-descending tiler." We also show that the hypercube cross unfolding made famous by Dali tiles space, but we leave open the question of whether or not it has an edge-unfolding that tiles the plane.
Cite
@article{arxiv.1512.02086,
title = {Hypercube Unfoldings that Tile R^3 and R^2},
author = {Giovanna Diaz and Joseph O'Rourke},
journal= {arXiv preprint arXiv:1512.02086},
year = {2015}
}
Comments
20 pages, 18 figures, 10 refs. Version 2: Corrected a typo, added a reference