Order-3-7 hexagonal honeycomb
In the geometry of hyperbolic 3-space, the order-3-7 hexagonal honeycomb or a regular space-filling tessellation with Schläfli symbol.
Geometry
All vertices are ultra-ideal with seven hexagonal tilings existing around each edge and with an order-7 triangular tiling vertex figure.Rendered intersection of honeycomb with the ideal plane in Poincaré half-space model | Closeup |
Related polytopes and honeycombs
It a part of a sequence of regular polychora and honeycombs with hexagonal tiling cells.Order-3-8 hexagonal honeycomb
In the geometry of hyperbolic 3-space, the order-3-8 hexagonal honeycomb or is a regular space-filling tessellation with Schläfli symbol. It has eight hexagonal tilings,, around each edge. All vertices are ultra-ideal with infinitely many hexagonal tilings existing around each vertex in an order-8 triangular tiling vertex arrangement.Poincaré disk model |
It has a second construction as a uniform honeycomb, Schläfli symbol, Coxeter diagram,, with alternating types or colors of tetrahedral cells. In Coxeter notation the half symmetry is = .
Order-3-infinite hexagonal honeycomb
In the geometry of hyperbolic 3-space, the order-3-infinite hexagonal honeycomb or is a regular space-filling tessellation with Schläfli symbol. It has infinitely many hexagonal tiling around each edge. All vertices are ultra-ideal with infinitely many hexagonal 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 hexagonal tiling cells.