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Thirds Cube Dissection, Many Styles, Liu Hui

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3D model description

Thirds Cube Dissection, Liu Hui's Cube Dissection

The cube can be sliced into three congruent pieces in many ways. One of the best known dissection dates back to 263 AD and Liu Hui's commentaries on the Nine Chapters of Mathematical Arts. In short, using a cube's (or cuboid's) diagonals, Liu Hui dissected the cube into 1 half, 1 third, and 1 sixth, known as "Qiandu," "Yangma," and "Bienao," respectively. For more information, please refer to .

The third-cube piece is most interesting. Obviously, it takes three copies to make a whole cube. Now, with 3D design, we can play with these mathematical gems in numerous ways and get the inside out. In this design, I provide several versions of the third cube. The cube is 50mm ^ 3.

Have fun and check out other cube dissections!

2. Bu, L. (2017). Exploring Liu Hui’s Cube Puzzle: From Paper Folding to 3-D Design. MAA Convergence. Accessible at

  • 3D file format: STL
  • Publication date: 2018/09/11 at 10:18



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STEAM educator, learning from and working with K-12 STEAM teachers to explore new ideas of teaching and engagement. I firmly believe ART is at the core of STEM learning or all human learning! I owe my ideas and designs to the hundreds of K-12 children and teachers and university professors I have had the pleasure of working with, in multiple disciplines-- math, science,engineering language arts, social studies, early childhood education and more! All mistakes, of course, are mine! There is no warranty or liability whatsoever implied or explicit behind the designs or ideas. They are all posted for their potential educational values.

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