The topology of the minimal regular cover of the Archimedean tessellations

TL;DR

This paper investigates the topological properties of the minimal regular cover surfaces for an infinite family of plane maps, including all Archimedean tessellations, revealing their underlying surface structures.

Contribution

It determines the topology of the minimal regular cover surfaces for all Archimedean maps, expanding understanding of their geometric and topological properties.

Findings

Identified the surface topology for the minimal regular covers of Archimedean tessellations.

Extended the topological classification to an infinite family of plane maps.

Provided a comprehensive description of the surface structures involved.

Abstract

In this article we determine, for an infinite family of maps on the plane, the topology of the surface on which the minimal regular covering occurs. This infinite family includes all Archimedean maps.