# Spinning the Cube: Face Diagonal & Hyperboloid

## 3D model description

### #Spinning the Cube: Face Diagonal & Hyperboloid

#### #Design to play with mathematics …

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 https://www.thingiverse.com/thing:3015098 ). 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. https://www.thingiverse.com/thing:2632180
2. https://www.thingiverse.com/thing:2993980
3. https://www.thingiverse.com/thing:2995638
4. https://www.thingiverse.com/thing:3071780
5. https://www.thingiverse.com/thing:1984059
6. https://www.thingiverse.com/thing:2430698
7. https://www.thingiverse.com/thing:2996971
• 3D model format: STL

## Creator

STEAM educator, learning from and working with K-12 STEAM teachers to explore new ideas of teaching and engagement. I firmly believe ART is at the core of STEM learning or all human learning! I owe my ideas and designs to the hundreds of K-12 children and teachers and university professors I have had the pleasure of working with, in multiple disciplines-- math, science,engineering language arts, social studies, early childhood education and more! All mistakes, of course, are mine! There is no warranty or liability whatsoever implied or explicit behind the designs or ideas. They are all posted for their potential educational values.

When working with children, please strictly observe all safety and health procedures! Please refer to the NSTA safety guides: http://www.nsta.org/safety/.

LGBU Contact: LGBU@SIU.EDU