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For questions about mathematical tiling.

95 votes
5 answers
4k views

Can a row of five equilateral triangles tile a big equilateral triangle?

Lee Mosher pointed me in the direction of Conway's theory of tiling groups. … Are there any high-level approaches other than the tiling groups? Or is a bare hands approach most likely to be successful?   …
Oscar Cunningham's user avatar
17 votes

How can one construct a four-coloring of a tiling of the plane with Smith, Myers, Kaplan, an...

So the unique 3-colouring of the hexagonal grid does indeed yield a 4-colouring of the original tiling. It remains to show that this colouring is the unique such. … Added 2023-06-14: The new Spectre tiling does not involve any flipped tiles. However we can still produce a similar colouring. …
Oscar Cunningham's user avatar