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Comment by penteract

Yeah, the seven cubes shape tiles R^3 by itself following the aperiodic tiling, but it also tiles R^3 in other ways, some of which are periodic. The bumps prevent any of the periodic tilings. See [1] for a better explanation with a picture of the shape as a rep-tile, and [2] for insight into how a rep-tile becomes an aperiodic tiling.

[1] https://arxiv.org/abs/2609.24779

[2] https://en.wikipedia.org/wiki/Rep-tile#Examples

parent penteract 17 days ago

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