In the geometry of hyperbolic 3-space, the order-6-infinite apeirogonal honeycomb (or ∞,6,∞ honeycomb) is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {∞,6,∞}.
It has infinitely many order-6 apeirogonal tiling {∞,6} around each edge.
All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many order-6 apeirogonal tilings existing around each vertex in an infinite-order square tiling vertex arrangement.

It has a second construction as a uniform honeycomb, Schläfli symbol {∞,(6,∞,6)}, Coxeter diagram, , with alternating types or colors of cells.
In the geometry of hyperbolic 3-space, the order-6-infinite apeirogonal honeycomb (or ∞,6,∞ honeycomb) is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {∞,6,∞}. It has infinitely many order-6 apeirogonal tiling {∞,6} around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many order-6 apeirogonal tilings existing around each vertex in an infinite-order square tiling vertex arrangement.
It has a second construction as a uniform honeycomb, Schläfli symbol {∞,(6,∞,6)}, Coxeter diagram, , with alternating types or colors of cells.
Order-6-4 square honeycomb