On January 1, 2007, I discovered an improved dissection of two dodecagons to one. Gone is the simplicity of my original dissection in favor of economy. The new dissection uses 20 pieces rather than the 26 in Figure 17.15. It draws inspiration from the 10-piece unhingeable dissection by Lindgren (1964b).
Those familiar with Lindgren's unhingeable dissection will recognize the shape of pieces B, E, H, L, O, and R. They may also notice that I divide the rest of the levels of the small dodecagons that contain those pieces into pieces that are somewhat reminiscent of pieces from Lindgren's dissection. But here the fun begins: I attach small equilateral triangles from the interior of the small dodecagons to certain pieces, and cut notches in the large pieces A and K to accommodate those triangles in the large dodecagon. I then glue the triangles created by cutting those notches onto pieces on the other level. The resulting triangular towers of the now 2-level pieces help to fill in the rest of the outer ring of the large dodecagon. Note that my new dissection is rounded.
Copyright 2007, Greg N. Frederickson.
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Last updated January 2, 2007.