I've started swatching, and it's going to be (hopefully) on size 7 needles. The yarn is knitting up beautifully, especially now I've stopped twisting the knit rows (thanks to Barbara for pointing that out; I figured out what I was doing wrong, and it was slowing me down as well - easily fixed, but I might use it for effect, and I'll deliberately keep doing it in the hat since I don't want to frog that) and it's giving me a lovely fabric. I may want to try some socks for myself in this yarn, once I've finished this project.
The intention is to knit up six swatches which are sufficiently off-square that when I felt them, they'll come out as near square as I can get them; then, I'll figure out what to do for pips (probably a contrasting yarn, felted), and then sew it up, stuff it, and let the cats at it.
Then, I'll start figuring out patterns to make triangles numbered from 1-8. That, I may not felt.
You'll know I've become really confident when I start doing patterns for pentagons numbered 1-12. That pattern, if I can pull it off, I shall type up and make available...