Air Puzzle

George W. Hart

Other Puzzles

This puzzle consists of four identical components that screw together.
It is made of nylon by selective laser sintering. The name comes from
Plato's association of the octahedron with the classical element of Air.
(I previously made a 2-part Fire puzzle and a 3-part Earth puzzle,
so guess what I'll be making next year.)

I made 105 of these as my IPP31 exchange puzzle.
Here it is all packaged up nicely.

Separately, the pieces look like this.  It is tricky to put them all together.

The key to the solution is to put three pieces together then start the fourth from the end, like this.

Here is the text on the sheet inside the box:

Air is a screw-together octahedron made of four identical nylon parts, dyed red, yellow, blue, and green. The name is taken from Plato’s proto-chemical mysticism, in which the octahedron represents the classical element of Air. It is split along four helicoid surfaces whose axes are aligned with a four-fold, long diagonal. I chose the helicoid pitch to make 1.5 revolutions.  It is in the series with my earlier Earth, and Fire puzzles.

This is one instance within a family of related screw dissections that others have also explored. Martin Gardner credits a related three-piece cube dissection to John E. Morse. [The Magic Numbers of Dr. Matrix, Prometheus Books, 1985, p. 319]  William Huff describes related forms used as exercises in an architectural design class. [William Huff, “Trisecting the Cube”]  Another three-piece screw-together cube, designed by Robert Reid in the 1980s and recently realized by Oscar van Deventer and George Miller, can be seen at  I came to appreciate the elegance of this family of forms after seeing a two-piece screw-together tetrahedron that Rinus Roelofs designed and brought to the 2005 Bridges Conference [].