This got the name Dodecagon Thing because it never turned into a real object. There are two versions that can be made with similar pieces and they can both be made to any size so could make cushions, afghans, or anything else. We made cushion size but never went any further.

We were introduced to this construction of a dodecagon at a Maths convention called MathsJam, in November 2011. Each speaker was allowed five minutes to present something they found interesting or challenging. Joel Haddley had been looking at shapes where you can double the area and get a new shape the same as the original but bigger.  He used a paper model for a nice visual proof of a dodecagon to fit the rule. I talked to him later ad he gave me the models he had used to illustrate his talk.

12 identical quadrilaterals can be joined to make a dodecagon  Some of the shapes have to be turned over but that doesn’t matter when they are knitted in garter stitch because they look the same on both sides. 24 of the same quadrilaterals can be joined to make a larger dodecagon, which is clearly double the area of the first.

Any design which consists of the same shape being used over and over can always be scaled up to become whatever size you want it to be. Changing the colours and arrangement of the shapes can give some interesting 3D effects.

To read more about the mathematics
Click here

To download the free pattern, read more about the afghan, and see more examples
Click here