120-Cell on Hypersphere, Stereographic Projection

This is a wireframe model of a stereographic projection into 3 dimensional space of a regular 4 dimensional regular solid, or 4-polytope, called the 120-cell or dodecaplex , which has been projected onto the circumscribed hypersphere. The 120-cell is the four dimensional analogue of the dodecahedron. It has a Schläfli symbol {5,5,3}, which means that the polygon faces of the cells have 5 equal sides, meeting 3 at a vertex, to form an dodecahedral cell, 3 of which meet around each edge in 4 dimensions. The figure in 4-space is 120 dodecahedral cells, all of whose vertices lie on a 4 dimensional hypersphere. All together the dodecaplex has 720 pentagonal faces, 1200 edges, and 600 vertices. The vertex figure (the shape exposed when a 4D corner is sliced off) is a tetrahedron, with 4 dodecahedrons meeting at each vertex. The 120 cell is one of the 6 regular convex polychora (a 4 dimensional regular polytope is also called a polychoron). The lengths of the edges are not preserved in this projection, but the angles between them are. The model has been made just large enough to be able to see the entire structure, and to be printable and strong enough to ship.