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Dodecagon Thing

Knitting
February 2012
This pattern is available as a free Ravelry download

A few months ago we went to a Maths convention and were intrigued by a simple proof that showed how the area of a dodecagon could be doubled to create a larger dodecagon.

It seemed an ideal candidate for translating to knitting. 12 identical shapes make the small dodecagon; 24 shapes make the larger version. Some of the shapes have to be reflected but this doesn’t matter in garter stitch as both sides look the same.

It is an interesting shape but limited in its usefulness as any tessellation beyond the 24 shapes creates a pattern with very jagged edges. 12, or 24, shapes can be used for a cushion or afghan. We are publishing it as a free pattern in the hope that someone can see potential for using it more imaginatively.

The shapes can be made to any size from very simple instructions. Some interesting optical effects can be created by the positioning of the colours.

  • Photos 1 and 2 show the two sides of the completed cushion.
  • Photos 3, 4 and 5 show different arrangements of the 24 pieces.
  • Picture 6 shows some colour combinations.
  • The final photo shows the paper version which was originally used to demonstrate the proof. (The photos are not to scale.)