There are six regular convex polytopes
in 4D, which are analogous to the
five Platonic solids in 3D. This is the fifth, the hyperdodecahedron, a remarkably beautiful object brought to my attention
by George Hart.
Here it's shown in a Schlegel diagram so you can see all
120 dodecahedral cells, though most are transformed by
perspective: in this projection, the only regular dodecahedra are the biggest one on the outside and the tiniest one at the center.
A bigger model is here
6.35 w x
6.664 d x
2.5 w x
2.624 d x