In the geometry of hyperbolic 5-space, the tesseractic honeycomb honeycomb is one of five paracompact regular space-filling tessellations (or honeycombs).
It is called paracompact because it has infinite vertex figures, with all vertices as ideal points at infinity.
With Schläfli symbol {4,3,3,4,3}, it has three tesseractic honeycombs around each cell.
It is related to the regular Euclidean 4-space tesseractic honeycomb, {4,3,3,4}.
It is analogous to the paracompact cubic honeycomb honeycomb, {4,3,4,3}, in 4-dimensional hyperbolic space, square tiling honeycomb, {4,4,3}, in 3-dimensional hyperbolic space, and the order-3 apeirogonal tiling, {∞,3} of 2-dimensional hyperbolic space, each with hypercube honeycomb facets.