The Platonic Compounds study explores all possible ways the five Platonic solids nest within each other. The research systematically examines compound configurations where multiple regular polyhedra share a common center, testing every geometric combination. The investigation addresses classical inscriptions like tetrahedra within cubes and octahedra within tetrahedra, as well as more complex interpenetrations. Each Platonic solid can be inscribed in or circumscribed about others through specific mathematical relationships. The study documents all geometrically valid nesting combinations. The research also explores these compounds as vertical tower configurations. Stacking arrangements scaled by golden ratio proportions create harmonic relationships between layers. The work exhausts combinatorial possibilities, establishing foundations for understanding how Platonic forms relate through nesting and vertical organization. This research later informed adaptations in larger installations.
Photography: Phillip C. Reiner
