2023 Bridges Conference Art Exhibition

# Doug Dunham, Lisa M Shier

## Artists

## Statement

My goal is to design aesthetic tessellating patterns on hyperbolic surfaces such as the Poincaré circle model or on surfaces of polyhedra. One set of polyhedra that we have considered are triply periodic polyhedra in Euclidean 3-space. The most regular ones are transitive on vertices, edges, and faces, and are often called skew apeirohedra. H.S.M. Coxeter and John Flinders Petrie proved that there are exactly three of these: {4,6|4}, {6,4|4}, and {6,6|3}, where {p,q|r} is composed of regular p-sided polygons meeting q at a vertex and with regular r-sided polygonal holes. We use the {6,6|3} for this patterned polyhedron. It is composed of invisible regular tetrahedral "hubs'' connected by "struts'' which are truncated tetrahedra.