EARTH Puzzle

George W. Hart

Other Puzzles



This puzzle consists of three identical components that screw together.
It is made of nylon by selective laser sintering. The name comes from
Plato's association of the cube with the classical element of Earth.




I made 101 of these as my IPP29 exchange puzzle.
Here it is all packaged up nicely.




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




The first step in the solution is to put together any two pieces like this, which is not hard.




The third must start in from a corner, like this.  Then it screws in left-handedly.




Here is the view looking down a 3-fold axis of symmetry.

Here is the text on the sheet inside the box:

EARTH  is a screw-together cube made of three identical nylon parts, dyed green, blue, and tan. The name is taken from Plato’s proto-chemical mysticism, in which the cube represents the classical element of Earth. It is split along three helicoid surfaces whose axes are aligned with a three-fold axis, i.e. a long diagonal of the cube. I chose the helicoid pitch to make 1.5 left-hand thread revolutions, which seems to make a good puzzle.

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”]  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 [www.bridgesmathart.org].  A different three-piece screw-together cube, designed by Robert Reid in the 1980s and recently realized by Oscar van Deventer and George Miller, is commercially available at puzzlepalace.com.  Earth has a different screw pitch and was designed without knowledge of theirs.