To make this zonohedron with Stella 4d (available as a free trial download here), start with a dodecahedron, and then perform a zonohedrification based on both faces and vertices. It is similar to …

This is a zonohedrified pentagonal prism. It has ninety rhombic faces, and they are based on the vertices of that prism. I made it using Stella 4d, which you can buy, or try for free, at

This is the icosahedron, one of the Platonic solids. It has twenty faces. The polyhedron below is the rhombic enneacontahedron, a well-known zonohedron with ninety faces. Finally, here is a polyhed…

In each odd dimension is a convex body - the polar zonoid - whose generating functions are trigonometric polynomials. The polar zonoid is a straightforward generalization of the polar zonohedron in dimension 3. The package has some applications of the polar zonoid, including the properties of configuration spaces of arcs on the circle and 3x3 rotation matrices. There is also a root solver for trigonometric polynomials.

This is the zonohedrification of the rhombicosidodecahedron. It is a zonohedron with 30 zones. Each zone consists of 58 edges, so the whole polyhedron has 58 × 30 = 1740 edges. Since all its faces are quadrilateral – actually they are all rhombuses – and each edge belongs to two faces, it must have 1740 × 4 / 2 = 870 faces. Since the polyhedron clearly has Euler characteristic 2, we may compute the number of vertices as 1740 - 870 + 2 = 872. - Zonohedrified rhombicosidodecahedron - Download Free 3D model by robinhouston