Transitive perfect colorings of the non-regular Archimedean tilings

TL;DR

This paper introduces a method to find minimal-color transitive perfect colorings of non-regular Archimedean tilings and explores their non-equivalent variants.

Contribution

It provides a systematic approach to obtain and classify minimal-color transitive perfect colorings for non-regular Archimedean tilings.

Findings

Method to determine least number of colors for transitive perfect colorings

Identification of non-equivalent colorings for given tilings

Application to various non-regular Archimedean tilings

Abstract

In this work, we give a method to obtain nontrivial transitive perfect colorings of the non-regular Archimedean tilings using the least possible number $n$ of colors. We also look for other non-equivalent transitive perfect $n$-colorings of a given non-regular Archimedean tiling.