Twin Spiky Stellated Dodecahedron, Infinity Cube, Magic Cube, Flexible Cube, Folding Cube, Yoshimoto Cube for for Flexible Filament Printing

Twin Spiky Stellated Dodecahedron, Infinity Cube, Magic Cube, Flexible Cube, Folding Cube, Yoshimoto Cube for for Flexible Filament Printing

Caveat: You could print the top or the bottom half. The top one has little to no stringing according to my experiments. Geometric ally, they are exactly the same up to flexing.

The Magic/Infinity Cube is a fascinating mathematical structure. More surprisingly, it can be further dissected into two sets of 8 half-cubes, each of which consists of 3 square pyramids. According to Reference 3, it was invented by Naoki Yoshimoto in 1971.

The half-magic cube flexes as the original magic cube does; it also folds beautifully into a 12-spike stellated dodecahedron. The top half and the bottom half are exactly the same, up to flexing. I have included both halves for those who are curious about a physical proof.
The half magic cube is not easy to design in a 3D environment, mainly because of the limitations of the structure and materials.

Traditionally, one uses adhesive tapes and cardboard or wood blocks. It works but does not feel good. After long hours of tinkering, I have designed a 3D model for printing with TPU flexible filament, taking advantage of what I did on previous projects using grooved connectors. It can be printed in one piece. The result goes beyond my expectations. It comes in three sizes: 20mm^3, 25mm^3, and 30mm^3. No, you don’t need both the top and the bottom pieces. They are exactly the same or, if you like, twins! You can snap two of them for the original magic cube, as shown in the pictures.

In light of the complex navigations and physical constraints, this should make an advanced design project for students. In my case, I first made a huge model using 48 polydron squares and adhesive tape before sketching them in Fusion 360. With parametric design, you could easily change its dimensions. Have fun!

References

https://www.math.nmsu.edu/~breakingaway/Lessons/MFC/MFC.html
https://www.chicaandjo.com/2008/05/08/magic-folding-wooden-photo-cubes/
http://www1.ttcn.ne.jp/a-nishi/y_cube/z_y_cube.html
https://blog.goo.ne.jp/ishihana427/e/0f8bb7f478edd956846a947f372fbac4