This page collects some material on puzzles made from symmetrically
arranged sticks. In the above example, the thirty sticks are
positioned on the edges of a dodecahedron, but rotated consistently.
The general idea is described in this paper which appeared in
the Bridges 2011
G. Hart, "Symmetric Stick Puzzles,"
Proceedings of Bridges Conference, 2011, pp. 357-364. (online
The paper describes software in Mathematica
for generating your own puzzles, which is available here.
The stl file for the above design is available on my makerbot page.
Some related stick-based puzzles based on the same underlying ideas
made with the same software are:
And I have other types of puzzle
designs online here.