On November 20, 2012, for each n = 1, 2, ... , I identified (4n+3)-piece folding dissections for a {(4n+2)} to two {(4n+2)/(n+1)}s.
I show a simple version for the case of n = 2 below, in which I convert a 1-level decagon to a 2-level 10-pointed star, using 11 pieces. The corresponding piano-hinged dissection would use double the number of pieces.
My dissection is reminiscent of Figure 13 in "Infinite families of monohedral disk tilings," by Joel Haddley, 2011. Haddley's figure shows 3 tilings of a disk by 20, 28, and 36 congruent curved figures. Haddley's constructions are lovely for their use of curved edges with respect to tessellations of disks. My dissections are natural within the realm of regular polygons and stars, reflecting the internal rhombic structure of such figures.
Copyright 2012, Greg N. Frederickson.
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Piano-hinged Dissections: Time to Fold!
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Last updated November 30, 2012.