Hart's Cube Puzzle

The puzzle was designed by Geoge Hart and published in one of
his puzzle pages: http://georgehart.com/Puzzles/CubePuzzle
It consists of two identical pieces that match to form a cube
by turning one piece in respect to the other. The two pieces are
separated by cutting the cube by a helicoid surface.
This code models a puzzle cube very similar to the Hart's one
but it is based just on his description and images and may be
a bit different.
The hardest part of the coding have been to deal with a constant gap between the pieces. I am in debt to Rudolf Huttary (http://www.thingiverse.com/Parkinbot/about) for his clever solution to the computation of the helicoid offset.
The stl files were generated for a 50mm cube. The code has some customizable parameters so you can create your own variant.