Author's Note: It's basic and traditional. You knit on DP needles. For worsted weight cotton (such as Sugar ' N' Cream), I use US 5 (3.75mm) needles. A set of 5 is much better for this than a set of 4. You work on 8 sections, with a YO at the beginning of each section on every other round. Then for a border, swithch to garter stitch and replace the YO with a M1. The "swirl" comes from having the increases unbalanced -- always at the same side of each section.
To be more specific:
Cast on 8 stitches.
Knit one round in the back of the stitches ( to tighten up the hole in the center).
Row 1: *YO, K1* 8 times.
Row 2: Knit around.
Row 3: *YO, K2*, 8 times.
Row 4: Knit around.
Row 5: *YO, K3*, 8 times.
Row 6: Knit around and so on until you have the size you want. For approx. 8 inches (what my DP needles will hold), go up to a total of about 120 stitches. This would put you at:
Next Row: *YO, K14*, 8 times.
Next Row: Purl around.
Next Row: *M1, K15*, 8 times.
Next Row: Purl around.
Next Row: *M1, K16*, 8 times.
Next Row: Purl around.
Cast off. When you weave in the thread at the beginning, use it to gather the starting stitches up tight.
Octagonal Swirl Cloth