120-Cell, Perspective Projection 1

This is a wireframe model of a perspective projection into 3 dimensional space of the regular 4 dimensional regular solid, or 4-polytope, called the 120-cell or dodecaplex. The 120-cell is the four dimensional analogue of the dodecahedron. It has a Schlafli symbol of {5,3,3}, which means that the polygon faces of the cells have 5 equal sides, meeting 3 at a vertex, to form a 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). Since the straight edges are preserved in perspective projection, they are not arcs, as they would be if the dodecaplex were first projected onto the hypersphere before projection into 3-space. The lengths of the edges and the angles between them are not preserved in this projection. This perspective projection is termed a Schlegel diagram of the polychoron, and the perpective projection point has been chosen far enough away to make the interior dodecahedra almost as large as the exterior ones.