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.
Diaz, Giovanna and O'Rourke, Joseph, "Hypercube Unfoldings that Tile R3 and R2" (2015). Computer Science: Faculty Publications, Smith College, Northampton, MA.