S. Louise Gould

This is an extension of the work I have done with fabric polyhedra. "The Symmetries of Things" written by Conway, Burgiel and Goodman-Strauss has provided many pathways to explore and it was the inspiration for this piece. This Archimedean infinite polyhedra is constructed of regular hexagons and squares. It illustrates the symmetry *642. Each vertex has 4 squares and one hexagon surrounding it. This model uses squares of four colors to show how the model moves into space. Each of the modules is constructed from a "net" of embroidered squares and hexagons. The nets were designed on Geometer's Sketchpad then digitized using 4-D Professional Software and stitched on a Viking Topaz embroidery sewing machine. The pictures show the object from three different directions.

This is the second in a series modeling infinite Archimedean polyhedra in embroidery and fabric. According to Conway, Burgiel and Goodman-Strauss in the Symmetries of Things, no one has yet enumerated the hundreds of Archimedean polyhedra in 3-space. Conway et al have however provided several for our exploration. This multiplied cuboctahedron dubbed “mucubocatahedron”with vertex configuration 6.4.6.4 illustrates many kinds of structure. This model draws attention to its tetrahedral symmetry, but it can also be trimmed to demonstrate both cubic and octahedral structures. The model is constructed from two congruent sets of chambers, each type with four hexagonal openings, but with inverted orientation. A journey down a corridor into a truncated octahedron chamber takes you from one truncated octahedron to another, colored or not depending upon which side of the surface your journey begins.