A small 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_large.pdf.
This is joint work with Saul Schleimer.