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Cube Spinning, Cage, Hyperboloid

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fe7d8da228fbb75bd6af5a06240c5d1e_display_large.jpg Cube Spinning, Cage, Hyperboloid
c36c5f2df4ce910680a7ec29092eb91e_display_large.jpg Cube Spinning, Cage, Hyperboloid
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858b2700c9a5f24093555759a0a41045_display_large.jpg Cube Spinning, Cage, Hyperboloid
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28ce60cfb9c6c210fac92a0625e87d10_display_large.jpg Cube Spinning, Cage, Hyperboloid
Cube_Cage_half25mm.stl Cube Spinning, Cage, Hyperboloid
Cube_Cage_whole_hardToPrint.stl Cube Spinning, Cage, Hyperboloid
Cube_EssentialEdges.stl Cube Spinning, Cage, Hyperboloid
Stand.stl Cube Spinning, Cage, Hyperboloid
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Creation quality: 5.0/5 (1 vote)
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  • Cube_Cage_half25mm.stl
  • Cube_Cage_whole_hardToPrint.stl
  • Cube_EssentialEdges.stl
  • Stand.stl

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Publication date 2018-10-15 at 08:46
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Published to Thingiverse on: 2018-10-12 at 21:59
Design number 34604
LGBU

LGBU

3D printer file info

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.

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