The 120-Cell

The 120-cell is composed of 120 dodecahedra. It is the equivalent of the 3D (pentagonal) dodecahedron. It is the dual of the 600-cell.

The structure of the 120-cell is nicely explained and illustrated on Savard's page on The Fourth Dimension (the description of the 120-cell begins part way down the page).

Russell Towle's Polytope page also contains a very nice projection of the 120-cell with hidden detail removed for clarity, and with the cells slightly “exploded” apart so that some of the internal structure of the projection can be seen.