Partial 120-Cell, Perspective Projection-75 cells

This is a partial wireframe model of a perspective projection into 3 dimensional space of the regular 4 dimensional solid, or polychoron, called the 120-cell or dodecaplex. In this model, only the innermost 75 cells are shown because including the larger cells makes it more difficult to see the inner structure, and more expensive. This partial model has 75 dodecahedral cells, with 470 vertices, 910 edges, and 516 faces. The full 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. The complete figure has 120 dodecahedral cells, all of whose vertices lie on a 4 dimensional hypersphere. All together the full dodecaplex has 720 pentagonal faces, 1200 edges, and 600 vertices. The vertex figure is a tetrahedron, which means that 4 dodecahedrons meet at each vertex. The 120 cell is one of the 6 regular convex polychora (regular 4-dimensional polytopes). 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 into 3-space is termed a Schlegel diagram of the polychoron, and preserves the shape (but not the size) of the faces, the number of cells around each edge (3), and the number of cells around a vertex (4), except where the 120-cell is cut at the outside edges of this partial projection.