Eve Torrence

This crocheted topological sculpture arises from crocheted chains arranged along the edges of a cube. The 6 four-sided openings correspond to the faces of a cube and the triangular surface regions correspond to the vertices. All twists in the surface are right-handed, i.e. clockwise. The surface has chiral octahedral symmetry. The boundary components form a polylink of four triangles with rounded vertices. The surface is orientable and is a Seirfert surface of this polylink. All the crochet sculptures on this page were created using techniques and patterns developed by Shiying Dong. Shiying and I are writing a book that will include directions for these models and many more. Our working title is "Unraveling Topological Crochet."

This sculpture was crocheted from chains arranged along the edges of an octahedron. The 8 three-sided openings correspond to the faces of an octahedron and the square surface regions correspond to the vertices. All twists in the surface are left-handed, i.e. counterclockwise. The boundary components form the same polylink, with the same chirality, as the boundary of the cube-based sculpture, but with more wavy edges. The dual sculptures required twists in the surface in opposite directions to create the same boundary link. This surface, unlike the cube-based surface, is non-orientable. Hence, we have two fundamentally different surfaces with the same boundary.

The mother in this pair of topological sculptures has 12 pentagonal holes and 20 triangular surface regions. The child has 20 triangular holes and 12 pentagonal surface regions. They can both be thought as an icosidodecahedron. Both surfaces have 6 boundaries, which are topologically equivalent to a polylink of 6 pentagons. The child contains the same number of stitches in essentially the same pattern as the mother. The triangular openings cause the child to be smaller. The boundary is forced to be wavy in order to fit the same number of stitches into the smaller footprint. The child snuggles easily inside the mother, but can also stand on its own. It is more playful than its rigid parent.

This crocheted surface was created from a starting chain lying along the edges of a rhombic dodecahedron. The surface has 8 triangular regions, 6 square regions, and 12 rectangular holes and resembles the rectification of the rhombic dodecahedron. If the holes were squares instead of rectangles, it would resemble a rhombic cuboctahedron. The surface has six boundaries, which come in parallel pairs. The boundaries are topologically equivalent to a polylink of six squares. Since all the holes have an even number of sides, this surface is orientable, hence it is a Seifert surface of this polylink.

This crocheted sculpture has 12 pentagonal holes, 20 triangular holes, and 30 square surface regions. It can be thought of as a rhombicosidodecahedron. It has 12 circular boundaries, each a different color. The boundaries are woven together in a pattern reminiscent of the Olympic rings.