Diagrams: Lindgren’s Dodecagon to Square Dissection

An interesting problem in plane geometry is to come up with a way to slice a certain type of polygon into pieces that can be reassembled into a different type of polygon with the same area. In 1951, Harry Lindgren showed an interesting way to dissect a regular dodecagon into six pieces that can be used to form a square.

Lindgren’s Dissection.

Since the angles in the pieces are either 45°, 60° or 150° (which equals 60° + 90°), and these are easily achieved by paper folding, I set out to create an origami version of this dissection puzzle. I was able to successfully create three modules matching Lindgren’s dissection. The seven-sided piece that consists of a square and three triangles is formed by combining two submodules. In the diagrams, I call the second submodule optional, since one could instead create a seven-piece dissection using an extra triangle module.

Thomas Cooper’s origami dodecahedron dissection. Folded and photographed by the author. See PDF diagrams.

Reference

Lindgren, H. “Geometric dissections.” Australian Mathematics Teacher 7 (1951): 7–10.