Filling space with hypercubes of two sizes -- The pythagorean tiling in higher dimensions

  title={Filling space with hypercubes of two sizes -- The pythagorean tiling in higher dimensions},
  author={Jakob Fuhrer},
We construct a unilateral lattice tiling of R n into hypercubes of two differnet side lengths p or q . This generalizes the Pythagorean tiling in R 2 . We also show that this tiling is unique up to symmetries, which proves a variation of a conjecture by B¨olcskei from 2001. For positive integers p and q this tiling also provides a tiling of ( Z / ( p n + q n ) Z ) n . 

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