Icosahedral Tilings Revisited

TL;DR

This paper offers a shorter proof that icosahedral tilings are characterized by finite configurations and proposes a potential weakening of the existing alternation condition.

Contribution

It provides an alternative, simpler proof of the characterization of icosahedral tilings and conjectures a possible relaxation of the alternation condition.

Findings

Shorter proof of tiling characterization

Conjecture on weakening the alternation condition

Enhanced understanding of tiling configurations

Abstract

Icosahedral tilings, although non-periodic, are known to be characterized by their configurations of some finite size. This characterization has also been expressed in terms of a simple alternation condition. We provide an alternative proof - shorter and arguably easier - of this fact. We moreover conjecture that the alternation condition can be weakened.