600-Cell, vertex centered, 1.5mm wires

The 600-cell, or icosaplex, is the 4D analog of the icosahedron, and is a convex 4 dimensional regular polytope, with Schlafli symbol {3,3,5}.. It has 120 vertices, 600 tetrahedral cells, 1200 triangular faces, and 720 edges. In this model, it is first projected onto the circumscribing hypersphere in 4D, then projected stereographically into 3D. The largest circles are the nearest edges to the projection point, which is centered on an edge just 'above' one vertex, near the 'north pole' of the hypersphere.  Because the projection point is not quite on the hypersphere, the angles are somewhat distorted, but the inner structure is brought nearer the outside, and is therefore clearer. From the outer icosahedron vertices, edges project only a short distance from the suface because the projection point is located off the sphere, rather than on it. If the projection point were on the hypersphere at {0,0,0,1}, instead of {0,0,0,1.13}, these edge cirlcles would be straight lines, with a center at infinity and returning to the opposite vertex, and the 600 cell, would fill all of 3 dimensional space. (The surface of a 4 dimensional sphere has 3 dimensions, and therefore can map to all of 3 dimensional space.) There are 12 edges at every vertex, and the vertex figure is an icosahedron.

The 'wires' of this model are 1.5 mm in diameter.