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

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The Cube Can Be Dissected In Multiple Ways. There Is One Well-Known Dissection That Decomposes A Cube (Or Any Rectangular Prism) Into Its Half, Third, And Sixth, Using Two Simple Face Diagonal Cuts. The Idea Dates Back All The Way To Around 263 Ad When A Famous Chinese Mathematician, Liu Hui, Illustrated The Idea In His Commentaries On The Chinese Nine Chapters Of Mathematical Arts. Liu Hui’S Dissection Can Be Easily Accomplished In A Modern 3D Design Environment Such As Autodesk Fusion 360® Or Similar Packages. Take A Cube. Slice It Along A Face Diagonal. We Get Two Halves. Each Half Is Called A “Qian Du,” Using Its Original Chinese Name. Keep A Half Piece And Slice The Other Along Another Face Diagonal. We 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 Natural Sense That Two Halves (Qian Du) Make A Cube And Three Yang Ma Make A Cube. The Bie Nao Are A Bit Unique. 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 A Whole Cube. It Is Fun To Explore The Visual, Spatial, And Quantitative Relationships Among These Pieces. For Printing, 0.2 Mm Is Just Fine. If You Choose 0% Infill, You Could Leave Some Small Magnets Inside, When The Pieces Are Half Way In The Printing Process. Please Increase Shell To 4 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

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