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.