Paul Schatz's Invertible Cube, Hexaflexagon

####Paul Schatz's Invertible Cube, Hexaflexagon

Please print the ring using flexible filament, starting with the "easy to print" version. The corners can be printed with PLA.

The Invertible Cube was discovered by Paul Schatz (1893-1979) and is one of those puzzles that are easier to make using paper than 3D printing. It is not hard to design from a cube, taking advantage of the symmetries. It is hard to print! After messing with it for a while, I was able to dissect a cube into a ring of six tetrahedra (a hexaflexagon) and two congruent corners. There are other ways to play with the corners, as I found.

To make the "invertible cube" printable, I added some connectors and pushed the inner faces back a little bit. The corner can actually serve as support for the ring; it can be printed without support. I also created another version with all the six tetrahedra sitting flat on the platform, which is much easier to print. Several files are included for diverse needs.

TPU flexible filament is recommended for an invertible cube. With PLA, one gets a model.

Of course, adhesive tapes can be used to connect the six tetrahedra. Observation: I found that even if the invertible cube is printed with all the pieces sitting on the bed, it wants to go back to a cube shape, once removed. That is pretty interesting. Please try the "easy-to-print" version first.

####References

1 Schatz, Paul (2013). The study of rhythms and technology : the evertible cube : polysomatic form-finding (4th Ed., P. Carline, Trans.). Niggli Publishers.

1. kaleidocycles. http://www.mathematische-basteleien.de/kaleidocycles.htm

2. https://mathcurve.com/surfaces.gb/orthobicycle/orthobicycle.shtml

3. https://truespring.wordpress.com/2013/02/14/who-was-paul-schatz/

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