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.