As of July 2019, this pattern now includes a cheat sheet to help you work a Non-Euclidian heel on any sock -- any stitch count (as long as it’s a multiple of 4) and any gauge!

Geometry was my favorite math class in high school; the logic of it just made more sense to me than any other math I’d taken. Even today, I am strangely satisfied by geometric patterns wherever I see them. Designing knitwear has offered me a new way to use geometry and challenged me to translate two-dimensional shapes into three- dimensional objects. This heel was borne of a desire to create a shape that was somewhere between a triangle and a pyramid to hug the back of the foot.

This sock pattern features a new take on the heel. It uses lifted increases to gently form a triangle of fabric that hugs the heel. The heel turn forms a second triangle under the heel and decreases the extra stitches. Although the pattern, as written, is for a stockinette sock, it is easy to insert the heel into any patterned sock using the same stitch counts.

To knit this pattern, you need to know how to:

• work in the round (using knit and purl),
• do lifted increases,
• do standard decreases (k2tog, ssk, p2tog), and
• use Kitchener stitch to graft live stitches.

Most people will need roughly 100 g of fingering weight yarn to knit a pair of these socks; actual yarn usage will depend upon the size made and the length of the foot. If you are knitting the largest size and/or have very long feet, you may require more than 100g. Please make sure you have enough yarn to complete your project.

Tech editing by eledixon

Looking for the toe-up version of this pattern? Take a look at CPCTC!