The bitruncation of the hypecube results in a polychoron composed of 16 truncated tetrahedra and 8 truncated octahedra. When the square faces are removed, the remaining 64 hexagons form a closed surface. This surface is hyperbolic with 4 hexagons meeting at a vertex. Topologically it is a torus with 17 handles. The 4-dimensional rotations takes us to 8 different cells, each of its own color.