Icosahedral Honeycomb

The icosahedral honeycomb is one of four regular space-filling tessellations (or honeycombs) in hyperbolic 3-space.

Three icosahedra surround each edge, and 12 icosahedra surround each vertex, in a regular dodecahedral vertex figure.

The dihedral angle of a Euclidean icosahedron is 138.2°, so it is impossible to fit three icosahedra around an edge in Euclidean 3-space. However in hyperbolic space, properly scaled icosahedra can have dihedral angles exactly 120 degrees, so three of these fit around an edge.

Read more about Icosahedral Honeycomb:  Related Honeycombs