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.
Related honeycombs
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}.
References
Order-4 24-cell honeycomb honeycomb Wikipedia(Text) CC BY-SA