This cowl is actually a mathematical object, and both addictive and quick to knit. (The test knitters said so!). It is a particular generalization of a Mobius band, made by extruding a Y to a sort of three-finned thing, then rotating one end by 1/3 and gluing it to the other end. The schematic at left, fourth image, gives a hint of this shape. (Mathematical details are given in an optional section of the pattern.) There is no other cowl, or for that matter, no other knitted anything, that is like this cowl!

The name comes from a technical description of the mathematical object’s construction. I had originally intended just to make a mathematical model, but when my prototype was done I realized it looked like a thin cowl… and thus I adapted it into a cowl pattern.

The purple-and-cream moss stitch cowl pictured here has been accepted into the juried 2013 Joint Mathematics Meetings Exhibit of Mathematical Art.

Any worsted-weight yarn will work for this cowl, and instructions are given for adapting the pattern to other yarn weights.

The pattern includes instructions for two different stitch patterns (moss and ribbing) in each of two sizes. There is no pattern-jog at the start/end of each round.

The shorter-size cowl requires about 200 yards of yarn; the longer-size cowl requires about 400 yards of yarn.

Finished measurements: Inner diameter 11 inches (23 inches for the longer-size cowl).
Inner circumference 22 inches (46 inches for the longer-size cowl).
Fin Depth 3 inches (3.5 inches for the longer-size cowl).

Special materials needed: Three size 7 circular needles, the shortest of which is 24 inches in length (36 inches for the longer-size cowl). It’s best if the three needles are differently colored.

Stitches and techniques needed: knit, purl, bind off.
The cast on needed to construct the cowl is unusual, and the pattern includes two ways to cast on. Both are accompanied by several diagrams.

For a scarf version of this pattern, see Y x I skinny scarves.

For a three-color skinny mathematical cowl, see Borromean Rings Cowl.