YxI: core, completion, and scarf
Materials and Methods: Core and completion are knitted with wool/soysilk blend yarn; core is augmented with floral wire; Scarf is knitted from Madelinetosh Tosh merino
Designer & Artist: sarah-marie belcastro
Year: 2012--2013
This collection was inspired by Example 1.29 on page 52 of Allen Hatcher's Algebraic Topology. The core is formed from the Cartesian product of an equilateral Y with an interval, where one end has been rotated by 2pi/3 before identifying the ends. The result is a nonmanifold generalization of a Mobius band. The boundary is wired so that the three fins of the Y are visible. The completion is formed by gluing a disc along the boundary of the core.
The core and completion were each constructed from the central circle outwards using a single strand of yarn. The major design challenge was creating a knitting cast-on that would produce three interlaced sets of free stitches (instead of the usual one or two sets). From this, one knits in the round for a few rounds to form the core, or for many rounds with decreasing to form the completion. Both items are made using stockinette stitch in order to highlight the different sides of the fabric as they meet in the central circle of the core. As a pair, it is most interesting to contrast the beauty of the core with the ugliness of the completion; often the beauty of mathematics is hidden within the structures.
The core is somewhat cowl-like, hence the artist has a pattern for such a cowl on Ravelry. As an alternative, the artist decided to make a scarf by doing the three-interlaced-sets-of-free-stitches cast on and then knitting across each set of stitches in turn.