Bridges 2011 Regular Paper
Symmetric Stick Puzzles
(Proceedings pages 357–364)
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.