Post #3078246

I worked with George Bell and made a puzzle: Dodecahedron Assembly Kit. There are 3 types of pieces. The challenge is to use some of them to assemble into a dodecahedron. The whole set can form two dodecahedra in at least 2 ways. There are even more ways to assemble some pieces into one dodecahedron with the leftover can't assemble together. Some of the assemblies have 2-fold, 3-fold and 5-fold symmetries, and some don't have any symmetry. Every assembly has its unique challenge. The 3 types of pieces are tightly related. The smallest pieces (bottom row) are the basic shape. I call them singles. The middle two rows are two singles connected together (doubles). The largest pieces are five singles connected together (quintuples). Each dodecahedron is formed by 20 single units. I analyzed the ways that the pieces can move. I'm visualizing them in this webpage: https://observablehq.com/d/008311b8a651406d There are 8 distinct motions. All the allowed motions are convex combinations of them.