Applications

So what can you do with these shapes?

If you're not into modular madness, then hats are a pretty obvious application as are bags, pillows and the like. Remember, as you increase out you can also decrease back down using the same formula -- this makes seamless polygonal pillows or potholders a very easy exercise.

If you're into modular stuff or are even slightly tempted, think about playing with the shapes. Yes, hexagons interlock, but hit some geometry web pages and tell me that you can't see some wonderful possibilities from "pentaflakes." Octagons can combine with triangles or other shapes and they can do so very traditionally (see Knitting Counter Panes by Mary Walker Phillips) or not so traditionally as part of a knitted patchwork or freeform piece.

To be a bit more mundane, consider the lowly patch pocket -- any of the square medallions would add a bit of style over and above your basic flat knit square. Or how about a pentagon "starfish" pocket?

Ponchos? Yup, polygonal ponchos are obvious. But what about an hexagon or octagon as the basic of a knitted skirt?

And there's always doily design and shawls with a slightly different shape.

And medallions can morph from one shape into another.

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