Order-6-4 triangular honeycomb
In the geometry of hyperbolic 3-space, the order-6-4 triangular honeycomb is a regular space-filling tessellation with Schläfli symbol.
Geometry
It has four triangular tiling around each edge. All vertices are ultra-ideal with infinitely many triangular tilings existing around each vertex in an order-4 hexagonal tiling vertex arrangement.Poincaré disk model | Ideal surface |
It has a second construction as a uniform honeycomb, Schläfli symbol, Coxeter diagram,, with alternating types or colors of triangular tiling cells. In Coxeter notation the half symmetry is = .
Related polytopes and honeycombs
It a part of a sequence of regular polychora and honeycombs with triangular tiling cells:Order-6-5 triangular honeycomb
In the geometry of hyperbolic 3-space, the order-6-3 triangular honeycomb is a regular space-filling tessellation with Schläfli symbol. It has five triangular tiling,, around each edge. All vertices are ultra-ideal with infinitely many triangular tilings existing around each vertex in an order-5 hexagonal tiling vertex arrangement.Poincaré disk model | Ideal surface |
Order-6-6 triangular honeycomb
In the geometry of hyperbolic 3-space, the order-6-6 triangular honeycomb is a regular space-filling tessellation with Schläfli symbol. It has infinitely many triangular tiling,, around each edge. All vertices are ultra-ideal with infinitely many triangular tilings existing around each vertex in an order-6 triangular tiling vertex arrangement.Poincaré disk model | Ideal surface |
It has a second construction as a uniform honeycomb, Schläfli symbol, Coxeter diagram, =, with alternating types or colors of triangular tiling cells. In Coxeter notation the half symmetry is = .
Order-6-infinite triangular honeycomb
In the geometry of hyperbolic 3-space, the order-6-infinite triangular honeycomb is a regular space-filling tessellation with Schläfli symbol. It has infinitely many triangular tiling,, around each edge. All vertices are ultra-ideal with infinitely many triangular tilings existing around each vertex in an infinite-order triangular tiling vertex arrangement.Poincaré disk model | Ideal surface |
It has a second construction as a uniform honeycomb, Schläfli symbol, Coxeter diagram, =, with alternating types or colors of triangular tiling cells. In Coxeter notation the half symmetry is = .