The Platonic Compounds study investigates all possible ways the five Platonic solids nest within each other. Compound configurations where multiple regular polyhedra share a common center are systematically documented, testing every geometric combination. Classical inscriptions — tetrahedra within cubes, octahedra within tetrahedra — and more complex interpenetrations are addressed alongside one another. Each Platonic solid can be inscribed in or circumscribed about others through specific mathematical relationships that determine vertex alignment, edge intersection, and face contact. Dual pairs and self-dual cases produce distinct compound behaviors. Vertical tower configurations extend the approach: stacking arrangements scaled by golden ratio proportions create harmonic relationships between layers, with circumradius ratios between successive solids governing the scaling sequence. All geometrically valid nesting and vertical organization combinations across the five solids are exhausted. The investigation remains ongoing.
Photography: Phillip C. Reiner
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