Cube Spinning, Cage, Hyperboloid

thingiverse

#### Spinning the Cube, Cage, Hyperboloid The cube is a fascinating mathematical object. If you spin it around a major diagonal, you get a pretty hyperboloid in the middle (see my other design at https://www.thingiverse.com/thing:3015098). Simple as it seems, it is a mathematically rich problem (see Hibert & Cohn-Vossen, 1952). Indeed, what really matters is not the whole cube, but the three critical edges as shown in the figure (also included as a STL file). Therefore, we could take advantage of 3D design techniques to make a simple version, hence the cube cage. It is hard to print the whole thing (included, though). However, we could slice the object into two congruent halves for printing. With a few drop of super glue, we could assemble the whole thing. A stand is also included for holding the cube cage for exhibit. #### Notes The cube cage half prints well without a raft on my printer. However, when bed adhesion is a problem, please consider use a thicker first layers or even a raft. Have fun! ##### References 1. Bu, L. (2018) https://www.thingiverse.com/thing:3015098 2. Hilbert, David, and S. Cohn-Vossen.1952. *Geometry and the Imagination*. Translated by P. Nemenyi. New York, NY: Chelsea Publishing Company.