Liu Hui Cube Puzzle/Dissection (Qiandu, Yangma, Bie'nao)

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The cube can be broken down into multiple sections. One well-known method breaks a cube (or any rectangular prism) into its halves, thirds, and sixths, using just two simple face diagonal cuts. This idea dates back to around 263 AD when the famous Chinese mathematician Liu Hui illustrated it in his commentaries on the Chinese Nine Chapters of Mathematical Arts. Liu Hui’s method can be easily done in a modern 3D design program like Autodesk Fusion 360 or similar software. Start with a cube. Slice it along a face diagonal to get two halves. Each half is called a "Qian Du" using its original Chinese name. Keep one half and slice the other along another face diagonal to get a square pyramid, which is one third of the cube and is called a "Yang Ma." The third solid is a tetrahedron, which is one sixth of the cube and is called a "Bie Nao." It makes perfect sense that two halves (Qian Du) make a cube and three Yang Ma make a cube. The Bie Nao are unique in their own way. If we take two Bie Nao and make a mirror image of one of them, the two Bie Nao would make a Yang Ma. Therefore, if we take six Bie Nao and mirror three of them, we could make three Yang Ma and further create a whole cube. It’s fun to explore the visual, spatial, and quantitative relationships among these pieces. For 3D printing, 0.2 mm is just fine. If you choose zero percent infill, you can leave some small magnets inside when the pieces are halfway through the printing process. Please increase the shell to four if the walls are too thin. For more information, please refer to Bu, L. (2017). Exploring Liu Hui’s Cube Puzzle: From Paper Folding to 3-D Design. MAA Convergence. Accessible at https://www.maa.org/press/periodicals/convergence/exploring-liu-hui-s-cube-puzzle-from-paper-folding-to-3-d-design