Platonic Compounds, 2022

The object of this project is to explore all cases of Platonic compounds. Platonic compounds are defined as compounds of regular polyhedra (tetrahedra, cubes, octahedra, icosahedra, dodecahedra) that share a common center. All combinations are explored. Cases of common Platonic compounds (tetrahedra nested in cubes, octahedra nested in tetrahedra) are recorded. Complex interpenetrations are recorded with classical Platonic compounds. Each Platonic compound is defined by mathematical relationships describing how the vertices, edges, and faces are interlaced. Different types of duals have different properties in this regard. Cases of vertically compounded Platonic polyhedra, created with scaled geometric scaling based on golden ratios, where the circumradius of one Platonic polyhedron is a scaled version of the circumradius of the other, are explored. All geometrically valid cases of vertically compounded arrangements of the 5 Platonic solids are recorded. Ongoing.