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:

This is joint work with Saul Schleimer.

A large version of the puzzle is available here.


IN: 2.457 w x 3.646 d x 0.561 h
CM: 6.242 w x 9.26 d x 1.424 h


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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
@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
@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
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
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
@unellenu: well done!
January 18, 2013, 1:35 am
Yay! I have just completed this puzzle. I visually love the sculptural form too :)
January 18, 2013, 1:30 am
Thanks for the shout-out Elisa!
October 12, 2012, 11:31 pm
We love this so much that we've featured it on Friday Finds! Check it out:
October 12, 2012, 4:17 pm


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