# Cube Spinning, Cage, Hyperboloid

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## 3D model description

#### 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. 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.

## 3D printer file information

• 3D design format: STL Folder details Close
• Cube_Cage_half25mm.stl
• Cube_Cage_whole_hardToPrint.stl
• Cube_EssentialEdges.stl
• Stand.stl

• Publication date: 2018/10/15 at 10:46

## 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

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