Order-4 Dodecahedral Honeycomb

In the geometry of hyperbolic 3-space, the order-4 dodecahedral honeycomb is one of four regular space-filling tessellation (or honeycombs). Four dodecahedra exist around each edge, and 8 dodecahedra around each vertex in an octahedral arrangement. Its vertices are constructed from 3 orthogonal axes. Its dual is the order-5 cubic honeycomb.

The dihedral angle of a dodecahedron is ~116.6°, so it is impossible to fit 4 of them on an edge in Euclidean 3-space. However in hyperbolic space a properly scaled dodecahedron can be scaled so that its dihedral angles are reduced to 90 degrees, and then four fit exactly on every edge.