"This stylish hat is formed from a single strip of 72 equilateral triangles," says Neatby. "The strip is folded and seamed using Mattress stitch. The brim and lining (optional for extra warmth) are worked in English Brioche stitch. Two contrasting yarns, a single colour or oddments may be used." You didn't expect a standard-issue assembly, did you? Neatby's inability to be boring or conventional is at full steam here. There's a terrific full-page chart and a schematic to guide you. Enormous fun for the enthusiast. A larger-gauge vest with similar construction is available here, and a beanie version of this technique is available here.
