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

28ce60cfb9c6c210fac92a0625e87d10_preview_featured.jpg Cube Dissection, Robert Reid, Three-Piece Puzzle, Liu Hui Cube Extension
92a7fcc156d39076ae423d1132e36a23_preview_featured.jpg Cube Dissection, Robert Reid, Three-Piece Puzzle, Liu Hui Cube Extension
f2cb06647ac2931cfdb146452bc0c300_preview_featured.jpg Cube Dissection, Robert Reid, Three-Piece Puzzle, Liu Hui Cube Extension
fe7d8da228fbb75bd6af5a06240c5d1e_preview_featured-1.jpg Cube Dissection, Robert Reid, Three-Piece Puzzle, Liu Hui Cube Extension
Reid_Cube_25mm.stl Cube Dissection, Robert Reid, Three-Piece Puzzle, Liu Hui Cube Extension
Reid_Cube_50mm.stl Cube Dissection, Robert Reid, Three-Piece Puzzle, Liu Hui Cube Extension
Reid_Cube_75mm.stl Cube Dissection, Robert Reid, Three-Piece Puzzle, Liu Hui Cube Extension
Reid_Cube_100mm.stl Cube Dissection, Robert Reid, Three-Piece Puzzle, Liu Hui Cube Extension
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Creation quality: 5.0/5 (1 vote)
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  • 3.3k views
  • 6 likes
  • 106 downloads
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3D design format
STL Folder details Close
  • Reid_Cube_100mm.stl
  • Reid_Cube_25mm.stl
  • Reid_Cube_50mm.stl
  • Reid_Cube_75mm.stl

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Publication date 2018-07-09 at 15:42
Design number 28324
LGBU

LGBU

3D printer file info

3D model description

Cube Dissection, Robert Reid, Three-Piece 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 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.

It is an interesting design and is slightly challenging mathematical manipulation in a 3D design environment like Fusion 360 ยฎ.

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
Print Settings

3D printing settings

Rafts:

No

Supports:

No

Resolution:

0.15-.2mm

Infill:

5-20%

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