The goal of this puzzle is to assemble the six identical "rib" pieces shown in the first picture into the cage-like structure shown in the others. This 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.
Each of the ribs is made from five dodecahedral (D) cells in the vertex (v) centered projection of the 120-cell to Euclidean space, and there are 6 ribs each of 5 dodecahedra (6x5=30). giving the puzzle its name.
Further description here: http://www.segerman.org/Dv30_Asteroid.pdf.
This is joint work with Saul Schleimer.