Heidi Burgiel
I practice mathematics because it is beautiful. Highly symmetric tilings, polyhedra and polytopes illustrate discrete groups acting on their native spaces. Colorings of these objects suggest subgroups and quotient spaces. In works like "Hyperbolic Afghan {3, 7}" we see glimpses of the kaleidoscopic landscapes described by algebraists.
"Hyperbolic Afghan {3, 7}" illustrates a tiling of the hyperbolic plane by triangles, 3 at a vertex, in crocheted cotton. Adapting techniques developed by Joshua and Lana Holden, the piece is not assembled from flat triangles but instead approximates constant curvature over its entire surface. Its coloration, inspired by William Thurston's rendition of the heptagon tiling underlying the Klein quartic, suggests the identifications required to construct that surface as a quotient of the hyperbolic plane.