Great Dirhombicosidodecahedron ("Miller's Monster")

The Great Dirhombicosidodecahedron, also known as "Miller's Monster," is a uniform polyhedron with 124 faces (24 pentagrams, 40 triangles, and 60 squares) meeting at 60 vertices, making it the only uniform polyhedron with 8 faces meeting at each vertex. A physical model of this complex shape requires 1,280 external facelets and nets spanning 42 A4 pages, with a diameter of approximately 30.6 centimetres.