Rhombicosidodecahedron Unpacked: A Deep Dive into Archimedean Geometry

In this episode we unpack the rhombicosidodecahedron, an Archimedean solid with 62 faces (20 triangles, 30 squares, 12 pentagons), 120 edges, and 60 vertices. We'll trace its kinship to the icosahedron and dodecahedron, show how it can arise from expanding an icosidodecahedron or assembling five cubes, and explain its link to Johnson solids through cupola rotations. We also explore the golden ratio in physical models, and visual tools like orthogonal projections, spherical tilings, and stereographic projections that illuminate its structure.

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