### 30-Cell Puzzle

Dyed and photographed by George Bell.
Dyed and photographed by George Bell.
Dyed and photographed by George Bell.

Since making the 30-cell puzzle, we have generalised and extended it to the Quintessence family of puzzles. Note that the Quintessence puzzles are at an incompatible scale to the 30-cell puzzle, due to the need to introduce pieces with relatively smaller dodecahedra than those that appear in the 30-cell puzzle.

The goal of this puzzle 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.

A large version of the puzzle is available here.

##### Tags:
Puzzles, Mathematical Art
cm: 6.242 w x 9.26 d x 1.424 h
in: 2.457 w x 3.646 d x 0.561 h

@gibell Yes, it has tetrahedral symmetry. It's based on the vertex centered projection of the 120-cell rather than the cell centered.
@henryseg Very cool! I see the "Twisted 30-Cell", the final shape looks quite different. I see tetrahedral symmetry in it, is that correct?
@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!
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.
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!
@unellenu: well done!
Yay! I have just completed this puzzle. I visually love the sculptural form too :)
Thanks for the shout-out Elisa!
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

• ##### White Strong & Flexible

White nylon plastic with a matte finish and slight grainy feel.

\$15.00