Bethe Ansatz solution of a decagonal rectangle triangle random tiling

TL;DR

This paper presents an exact Bethe Ansatz solution for a decagonal rectangle-triangle random tiling, providing insights into its entropy maximization similar to other known quasicrystalline tilings.

Contribution

It introduces a Bethe Ansatz solution for a new decagonal tiling, extending methods used for other quasicrystalline tilings to this specific case.

Findings

Exact expression for the maximum entropy of the decagonal tiling

Extension of Bethe Ansatz solutions to new tiling geometries

Comparison with known dodecagonal and octagonal tilings

Abstract

A random tiling of rectangles and triangles displaying a decagonal phase is solved by Bethe Ansatz. Analogously to the solutions of the dodecagonal square triangle and the octagonal rectangle triangle tiling an exact expression for the maximum of the entropy is found.