Order-6-4 triangular honeycomb

In the geometry of hyperbolic 3-space, the order-6-4 triangular honeycomb is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {3,6,4}.

Geometry
It has four triangular tiling {3,6} around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many triangular tilings existing around each vertex in an order-4 hexagonal tiling vertex arrangement.

It has a second construction as a uniform honeycomb, Schläfli symbol {3,61,1}, Coxeter diagram,, with alternating types or colors of triangular tiling cells. In Coxeter notation the half symmetry is [3,6,4,1+] = [3,61,1].

Related polytopes and honeycombs
It a part of a sequence of regular polychora and honeycombs with triangular tiling cells: {3,6,p}

Order-6-5 triangular honeycomb
In the geometry of hyperbolic 3-space, the order-6-3 triangular honeycomb is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {3,6,5}. It has five triangular tiling, {3,6}, around each edge. All vertices are ultra-ideal (existing beyond the ideal boundary) with infinitely many triangular tilings existing around each vertex in an order-5 hexagonal tiling vertex arrangement.

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

It has a second construction as a uniform honeycomb, Schläfli symbol {3,(6,3,6)}, Coxeter diagram, =, with alternating types or colors of triangular tiling cells. In Coxeter notation the half symmetry is [3,6,6,1+] = [3,((6,3,6))].

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

It has a second construction as a uniform honeycomb, Schläfli symbol {3,(6,∞,6)}, Coxeter diagram, =, with alternating types or colors of triangular tiling cells. In Coxeter notation the half symmetry is [3,6,∞,1+] = [3,((6,∞,6))].