Symmetric Stick Puzzles

George Hart
Proceedings of Bridges 2011: Mathematics, Music, Art, Architecture, Culture (2011)
Pages 357–364 Regular Papers


A large family of beautiful mechanical puzzles is based on the idea of positioning identical sticks symmetrically in space on the 2-fold axes of a polyhedral symmetry group. Many of these designs have a visual richness that gives them a sculptural quality. Structures in this family can differ in terms of the symmetry group chosen, the amount of rotation of the sticks about the axis, the length, cross sectional shape, and end treatment of the sticks, among other parameters. In certain designs, some sticks are fused together into compound parts. In addition, wherever two parts would intersect, a notch is made in one to make space for the other, and there are many options for how that choice is made throughout the puzzle.

This family of designs is explored and a simple method is presented for the reader to produce a wide variety of new puzzles. A short program written in Mathematica is used to explore designs in this parameter space and produce the overall stick geometry. Then a separate 3D editing program (e.g., Rhino) provides the constructive solid geometry operations that join the sticks, create the notches, and/or shape the stick ends. Finally, a 3D printer is used to fabricate the components. In the examples below, I use an inexpensive Makerbot to produce plastic versions of the puzzles at minimal cost. Several examples are presented of this overall process.