24-cell ortho F4

This is a wireframe model of a perspective projection into 3 dimensional space of the vertices of a regular 4 dimensional regular solid, or 4-polytope, called the 24-cell or octaplex. The 24-cell (also called the icositetrachoron, polyoctahedron, or hyperdiamond) is the four dimensional analogue of the octahedron, a regular 3D Platonic solid. It has a Schläfli symbol {3,4,3}, which means that the polygon faces of the cells have 3 equal sides, meeting 4 at a vertex, to form an octahedral cell, 3 of which meet around each edge in 4 dimensions. The boundary of the figure is 24 octahedral cells. All together the, octaplex has 96 triangular faces, 96 edges, and 24 vertices. The vertex figure (the shape exposed when a 4D corner is sliced off) is a cube, with 6 octahedra meeting at each vertex. The 24-cell is the unique convex self-dual regular Euclidean polytope which is neither a polygon nor a simplex.  Due to this singular property, it does not have a good analogue in 3 dimensions. . It is one the 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 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 orthographic projection produces the F4 Petrie polygon when viewed from above, with 12-fold rotational symmetry.