Spherical embeddings of symmetric association schemes in 3-dimensional Euclidean space

TL;DR

This paper classifies symmetric association schemes that can be faithfully embedded in 3D Euclidean space, expanding understanding of their geometric representations.

Contribution

It provides a complete classification of symmetric association schemes with faithful 3D spherical embeddings, based on prior work on primitive schemes with specific parameters.

Findings

Complete classification of schemes with 3D spherical embeddings

Identification of conditions for faithful embeddings

Extension of previous primitive scheme research

Abstract

We classify the symmetric association schemes with faithful spherical embedding in 3-dimensional Euclidean space. Our result is based on previous research on primitive association schemes with $m_1 = 3$.