Rectified 24-Cell, Stereographic Projection

When the midpoints of the 96 edges of the 4-dimensional 24-cell are used as vertices of a new polytope, or 4D polyhedron, we get the "rectified, or truncated, 24-cell". It is projected first onto the circumscribing hypersphere in 4D, which results in the edges being circular arcs, then it's projected into 3-space as a wire-frame model from a point at the 'north pole':({0,0,0,1}. It has 288 edges, and consists of 48 cells: 24 cubes, and 24 cuboctahedra. In 4D, all of the vertices are equidistant from the center; the inner ones in the 3D projection are just farther away from the 'north pole' projection point. This projection does not preserve edge length, but it does preserve the edge intersection angles. The 'wires' are 1.5 mm in diameter, and there is a larger model available.