Meadows in the Heptgrid and Possible Generalizations

Abstract

In this paper, we summarize the results about flowers in the heptagrid, the tessellation $(7,3)$ of the hyperbolic plane, results presented for MCU'2024 at Nice, France. In particular, we define meadows, more precisely $n$-meadows for any integer $n$ at least 3. We recall that for each integer $n$ at least three, there is an $n$-meadow on the heptagrid. We suggest that those results can be generalized to tilings $(p,3)$ of the hyperbolic plane, where $p\geq 7$.

Keywords

• hyperbolic geometry
• tilings
• flowers
• meadows