Artfully Folding Hexagons, Dodecagons, and Dodecagrams

Greg Frederickson
Proceedings of Bridges 2013: Mathematics, Music, Art, Architecture, Culture (2013)
Pages 135–142


Folding dissections are introduced for hexagons, dodecagons, and dodecagrams. Each folding dissection transforms one of these figures to a similar figure but of a different height. The goal is to minimize the number of pieces in the folding dissection, while at the same time exploiting symmetry to create beautiful objects that fold magically before our eyes. For regular hexagons, the dissections transform a regular hexagon of height h to a regular hexagon of height nh, where n is, in turn, 3 or 4 or 9 or 16 or 25. For regular dodecagons, our dissection transforms one dodecagon to another twice as high. For the 12-pointed star {12/2}, we give a dissection to a star 3 times as high, and also one to a star twice as high. The design of these various folding dissections is explored.