Eve Torrence

All these crocheted surfaces have the same boundaries: two unknots linked through each other twice, i.e. a Whitehead link. All are unique, but there are only three surface types up to homeomorphism. The four green surfaces are homeomorphic to a torus (with two punctures), the two purple surfaces are homeomorphic to a Klein bottle (with two punctures), and the yellow surface is homeomorphic to a Mobius band (with one puncture). If the boundaries of two surfaces are the same colors, they were designed from the same Whitehead link diagram using different algorithms. The diagram is reflected in the shape of the boundaries, which look like an 8 and an oval (black and white), two 8s (blue and yellow), or two boomerangs (purple and lavender).

This topological crochet sculpture has eight boundaries that form a polylink of eight triangles. The underlying structure is a rectification of a chamfered cube. A chamfered polyhedron is formed by shaving off the edges of a polyhedron and replacing each edge with a hexagon. The chamfered cube has six square and twelve hexagonal faces. A rectification is formed by truncating each vertex to the midpoint of the adjacent edges. The result in this case is a polyhedron with six square, twelve hexagonal, and 32 triangular faces. This surface is orientable with genus 5, thus it is homeomorphic to a five-hole torus with eight punctures.