Order-7 dodecahedral honeycomb

In the geometry of hyperbolic 3-space, the order-7 dodecahedral honeycomb is a regular space-filling tessellation (or honeycomb).

Geometry
With Schläfli symbol {5,3,7}, it has seven dodecahedra {5,3} around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many dodecahedra existing around each vertex in an order-7 triangular tiling vertex arrangement.

Related polytopes and honeycombs
It a part of a sequence of regular polytopes and honeycombs with dodecahedral cells, {5,3,p}.

It a part of a sequence of honeycombs {5,p,7}.

It a part of a sequence of honeycombs {p,3,7}.

Order-8 dodecahedral honeycomb
In the geometry of hyperbolic 3-space, the order-8 dodecahedral honeycomb a regular space-filling tessellation (or honeycomb). With Schläfli symbol {5,3,8}, it has eight dodecahedra {5,3} around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many dodecahedra existing around each vertex in an order-8 triangular tiling vertex arrangement.

It has a second construction as a uniform honeycomb, Schläfli symbol {5,(3,4,3)}, Coxeter diagram,, with alternating types or colors of dodecahedral cells.

Infinite-order dodecahedral honeycomb
In the geometry of hyperbolic 3-space, the infinite-order dodecahedral honeycomb a regular space-filling tessellation (or honeycomb). With Schläfli symbol {5,3,∞}. It has infinitely many dodecahedra {5,3} around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many dodecahedra existing around each vertex in an infinite-order triangular tiling vertex arrangement.

It has a second construction as a uniform honeycomb, Schläfli symbol {5,(3,∞,3)}, Coxeter diagram,, with alternating types or colors of dodecahedral cells.