Exploration of unit distance graphs

Finite graph Cartesian productions of triangles result in the class of graphs (K3)n. Several models were used to study the properties of this class of graphs, primarily a ternary numbering system and embeddings on a multi-dimensional torus. The properties explored focused on maximality as a unit distance graph, rigidity and motion, and subgraphs. An original Java application was written to explore the degrees of freedom and generate unit distance realizations in the plane