## Self-similar periodic tilings on the Heisenberg group.(English)Zbl 0829.22018

Let $$G$$ be the Heisenberg Lie group. The author constructs a tiling on $$G$$, so that the discrete cocompact subgroup consisting of all elements of $$G$$ with integral coordinates, acting on $$G$$ by left multiplication, acts freely and transitively on the set of tiles.

### MSC:

 22E40 Discrete subgroups of Lie groups 53C20 Global Riemannian geometry, including pinching

### Keywords:

self-similar periodic tilings; Heisenberg Lie group; tiling
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