30-Cell Puzzle

Design by henryseg

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(9) Comments

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A large version of the puzzle is available here.

The goal is to assemble the five identical pieces shown in the first picture into the ring-like structure shown in the others. Each of the five pieces is made from six dodecahedral cells, giving the puzzle its name. It is based on the 120-cell, one of the six regular polytopes in four-dimensional space. When assembled the puzzle is a part of the stereographic projection of the radial projection of the 120-cell to the three-sphere.

Further description here: http://www.segerman.org/30-cell_puzzle.pdf.

This is joint work with Saul Schleimer.

cm: 6.242 w x 9.26 d x 1.424 h

in: 2.457 w x 3.646 d x 0.561 h

Comments

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henryseg says:

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@gibell Yes, it has tetrahedral symmetry. It's based on the vertex centered projection of the 120-cell rather than the cell centered.

April 23, 2013, 11:26 pm

gibell says:

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@henryseg Very cool! I see the "Twisted 30-Cell", the final shape looks quite different. I see tetrahedral symmetry in it, is that correct?

April 23, 2013, 6:31 pm

henryseg says:

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@gibell Yes, the flexibility is essential. I made a large experimental version in stainless steel for someone, and unfortunately it seems to be unsolvable (hence why I never made that version public). By the way, a big update on extensions and variations of this puzzle is coming soon!

April 23, 2013, 3:25 pm

gibell says:

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It is not clear to me if this puzzle could be taken apart if the pieces were rigid. The flexibility of the plastic seems useful, and perhaps even necessary.

April 23, 2013, 3:20 pm

gibell says:

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Very nice puzzle! At first I tried to assemble it without looking at any photos - I was unsuccessful. After peeking at a photo of the assembled puzzle, I figured out how two pieces seat against one another. But it is still tricky to get that last piece in place. Bravo, Henry!

April 23, 2013, 3:18 pm

henryseg says:

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@unellenu: well done!

January 18, 2013, 1:35 am

unellenu says:

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Yay! I have just completed this puzzle. I visually love the sculptural form too :)

January 18, 2013, 1:30 am

henryseg says:

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Thanks for the shout-out Elisa!

October 12, 2012, 11:31 pm

ElisaRichardson says:

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We love this so much that we've featured it on Friday Finds! Check it out: http://www.shapeways.com/blog/archives/1680-Friday-Finds-3D-Printed-Designs-From-the-Shapeways-Community.html

October 12, 2012, 4:17 pm