English

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

R2 v1 2026-06-22T12:03:20.893Z