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arXiv · 1512.02086

Hypercube Unfoldings that Tile R^3 and R^2

Giovanna Diaz·Joseph O'Rourke
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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.

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Giovanna Diaz, Joseph O'Rourke. 2015-12-07. Hypercube Unfoldings that Tile R^3 and R^2. https://arxiv.org/abs/1512.02086

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