S. Louise Gould

The Semi-snub Mucube (ssμC) 4.3.4.3.3.3 is the most recent in a series of infinite space filling polyhedra. The surface of this Archimedean polyhedron separates space into two congruent parts. The tunnels travel from one cuboctahedral chamber to another. There are also octahedral chambers which alternate between bulging from one side to the other. The doorways to the tunnels are skewed hexagons. The four squares around the perimeter of a cuboctahedral chamber alternate between left and right orientations. A diagram for the lattice for the polyhedron can be found on page 337 of The Symmetries of Things.

In The Symmetries of Things, Chaim Goodman-Strauss notes “The Archimedean solids and their duals can be nicely arranged so that their edges are mutually tangent, at their intersections, to a common sphere. Three are the dual Platonic solids, plus one of them, the dual tetrahedron and its identical dual with the sphere passing through the intersections. The others are Archimedean solids, some of the “kis-cousins”: the truncated Tetrahedron and its dual the kisTetrahedron, the truncated Octahedron with its dual the kisCube, and the Truncated Cube and its dual the kisOctahedron. As with tessellations in the plane, in space the Platonic solids have Platonic duals and the Archimedean solids have duals with faces that are not regular polygons.