Six-Stick Puzzle

George W. Hart

This is an example in my series of symmetrically arranged stick puzzles.  In the above example, there are eighteen sticks positioned on the edges of a truncated tetrahedron (TT). I found that it is impossible to communicate the structure with just a single image, so I hope you find this jumpy, flickering animation to be more useful than annoying.

Here is the same object viewed so it is aligned with the axes. The angle of stick rotation about their centers was chosen to be 45 degrees relative to the underlying TT, so opposite sticks on each 2-fold axes are parallel. This makes it tricky to see how it it is derived, but observe that the four large non-convex hexagons and four small triangles are arranged exactly as in a TT.  You can also see that my Makerbot isn't terribly precise, but it works well enough.

The eighteen sticks are grouped into six identical sets of three that are fused into 3D zig-zags that are centered on the positive and negative XYZ axes. In this respect, it is related to traditional six-piece burrs, except that the mating parts are external rather than internal.

You may be able to see the structure more clearly from this animation. Here, it rotates about a 2-fold axis.  (In the image at the top of the page, it rotates about a 3-fold axis.) Starting from this underlying design, I shortened and rounded the free ends of the sticks and made a notch at the crossings. The stl file is available on my Makerbot page.  And I have more puzzle designs online here.