In the geometry of hyperbolic 5-space, the order-4 24-cell 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 {3,4,3,3,4}, it has four 24-cell honeycombs around each cell.
It is dual to the tesseractic honeycomb honeycomb.
It is related to the regular Euclidean 4-space 24-cell honeycomb, {3,4,3,3}, as well as the hyperbolic 5-space order-3 24-cell honeycomb honeycomb, {3,4,3,3,3}.