Spinning the Cube: Face Diagonal & Hyperboloid

thingiverse

It is fun and beautiful to spin a cube and ponder about the mathematics! We can spin a cube on a vertex for a pretty solid (see my designs www.thingiverse.com/thing3015098). How about spinning the cube around an axis that connects the centers of two opposite faces? Kind of boring. It is a cylinder. Well, how about spinning a face diagonal? Well, that becomes more interesting! We get, again, a hyperboloid. In playing with the design, I see that the shape obtained when spinning a face diagonal makes a great container for the cube itself or, even better, for a dissected/trisected cube (see my cube dissection/trisection designs). I have included the famous cube trisection model by Liu Hui (ancient Chinese mathematician), which can be printed in one piece, if you like, with the shell. Otherwise, one can print three copies of the third-cube. In fact, any 50-mm cube can be put in the middle. Some tolerance is included in the design. My cube dissection/trisection designs: 1. www.thingiverse.com/thing2632180 2. www.thingiverse.com/thing2993980 3. www.thingiverse.com/thing2995638 4. www.thingiverse.com/thing3071780 5. www.thingiverse.com/thing1984059 6. www.thingiverse.com/thing2430698 7. www.thingiverse.com/thing2996971