Trisection of a cube

by Erikjuh, published

Trisection of a cube by Erikjuh Jan 10, 2015


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Three equal parts form a cube. The fit is perfect, assembly can be challenging. I have reverse engineered the "Cubic Trisection", invented by Robert Reid and designed by Oskar van Deventer.

Update: Added a version with a 0.4 mm gap between the assembled parts to make up for printer inaccuracies.


Added a version with a 0.4 mm gap between the parts. If you know you printer is very accurate, use the original one. Otherwise, or if you found the original one won't fit, use the one with the bigger tolerance.

The model is sized to form a 5 cm cube. I printed it at 80% scale to save some time. Just scale it to your liking and print three pieces.

Printer: Zortrax M200
Layer height: 0.14 mm
Print time (per piece): 1h16
Infill: Light

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I think print size matters, printed at 76% and was too tight, larger tolerance printed fine, then printed full size with the larger tolerance and it seemed too loose. Nice design though, fun to play with.

could this be an openscad model with adjustable margin?

Probably, but I have no experience with openscad.

Very nice, thanks for sharing

Printed at 1.5 scale on a stratasys. Took a good bit of sanding, but worked out great. Recommend using the looser tolerance files for any printer with less that stratasys tolerances. Very cool!

Suggest calling it a "Cube Root"??

Works amazingly well!! didn't even need supports. =D

Mind posting your soldiworks file? I tried to model this for ages but never quite achieved it. Cheers

Excellent design! This worked great! I had to sand of some surface pimples from the "scaffolding" in the vertical bend. I fits perfectly!

lol yup, that's where I first saw it.

As George W. Hart (Dept. Computer Science, Stony Brook University, http://www.georgehart.com) mentioned,
others have previously designed related forms. Martin Gardner credits a related three-piece cube
dissection to John E. Morse [1]. William Huff describes related forms used as exercises in an
architectural design class [2]. A 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
[3]. I came to appreciate the elegance of this family of forms after seeing a two-piece screw-together
tetrahedron that Rinus Roelofs [4] designed and brought to the 2005 Bridges Conference [5].

[1] Martin Gardner, The Magic Numbers of Dr. Matrix, Prometheus Books, 1985, p. 319
[2] William Huff, “Trisecting the Cube,” http://www.mi.sanu.ac.yu/vismath/visbook/huff
[3] George Miller, http://www.puzzlepalace.com
[4] Rinus Roelofs, http://www.rinusroelofs.nl
[5] Bridges Conference Exhibit photos, http://www.bridgesmathart.org/pic.html