Six Dimensional Cube

This model represents a 3-dimensional shadow of the regular 6-dimensional cube (or, more properly, its edges and vertices).  This particular shadow has icosahedral symmetry.  This achieved by mapping the 6 zones of the 6-dimensional cube isometrically to the 6 zones of the rhombic triacontahedron.  Thus, the convex hull of this figure is the rhombic triacontahedron.