### Infinite Polyhedra---Murhombicuboctahedron (6.4.4.4) and Mucuboctahedron (6.4.6.4)

Materials and Methods: Sewn and Embroidered Fabric and Felt

Designer & Artist: S. Louise Gould

A discussion of infinite polyhedra in *The Symmetries of Things*, by Conway, Burgiel and Goodman-Strauss, inspired the artist to explore infinite Archimedean polyhedra. First came the embroidered fabric model of the murhombicuboctahedron with vertex configuration (6.4.4.4). The second in this series is an embroidered felt version of the mucuboctahedron (6.4.6.4).

The murhombicuboctahedron (6.4.4.4) seemed a rather straightforward model with its chambers and tunnels arranged in a tidy cubical array, although the source of its name is somewhat baffling. The mucuboctahedron on the other hand features paired chambers of truncated octahedral chambers. The two chambers have hexagonal faces colored blue, yellow, purple and red in the same order on the outside but are oriented at a 120-degree rotation from each other. This has the effect of staggering the chambers. Depending upon where the infinite polyhedron is trimmed the mucuboctahedron shows several different patterns. A cubic structure reflects its basic lattice structure. Other views show an octahedron and a ring of cells that moves about a central hexagon; yet, the sewn presentation clearly shows that the structure can be seen as tetrahedral. So we have one infinite polyhedron that presents itself in at least 4 different ways depending upon how we look at it.