Face embeddings of Archimedean solids

TL;DR

This paper characterizes Archimedean solids among convex uniform polyhedra using face embeddings into a regular tetrahedron, providing a proof for a previously unproven listing.

Contribution

It offers a formal proof for the classification of Archimedean solids via face embeddings, filling a gap in the existing literature.

Findings

Archimedean solids can be characterized by face embeddings into a regular tetrahedron

Provides the first formal proof for the listing of Archimedean solids

Enhances understanding of polyhedral embeddings in geometric topology

Abstract

We characterize the Archimedean solids among the convex uniform polyhedra via face embeddings into a regular Tetrahedron. This result has been listed without proof in the literature.