Cube Dissection, Robert Reid, Three-Piece Puzzle, Liu Hui Cube Extension by lgbu

Last crawled date: 3 years, 2 months ago

Cube Dissection, Robert Reid, Three-Piece Zigzag Puzzle, Liu Hui Cube Extension
Yet another way to dissect a cube into three congruent pieces. It takes three copies to make a cube. It is simple to assemble with a gentle twist. There are four sizes provided. The 50mm^3 one is recommended.
This dissection can be credited to Robert Reid in recent history (see URL below). To me, it seems to be an extension of the cube-dissecting method of Liu Hui (263 AD, Chinese mathematician), who detailed a 1/2, 1/3, 1/6 dissection of a cube (or, in general, a cuboid) in his Nine Chapters on Mathematical Art. The famous Liu Hui dissection is the end case of a family of infinitely many such designs, I think. I am pretty sure it is not unique! In this specific design, I used the midpoints of certain edges and diagonals. The critical point of dissection used is a centroid.
It is an interesting design and is slightly challenging mathematical manipulation in a 3D design environment like Fusion 360 ®.
Have fun playing with math and art!
References
Reid, Robert. http://www.martinhwatson.co.uk/robert_reid.html
Bu, Lingguo. https://www.maa.org/press/periodicals/convergence/exploring-liu-hui-s-cube-puzzle-liu-hui-s-principle
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