Order-7 dodecahedral honeycomb
In the geometry of hyperbolic 3-space, the order-7 dodecahedral honeycomb is a regular space-filling tessellation.
Geometry
With Schläfli symbol, it has seven dodecahedra around each edge. All vertices are ultra-ideal with infinitely many dodecahedra existing around each vertex in an order-7 triangular tiling vertex arrangement.Poincaré disk model Cell-centered | Poincaré disk model | Ideal surface |
Related polytopes and honeycombs
It a part of a sequence of regular polytopes and honeycombs with dodecahedral cells,.It a part of a sequence of honeycombs.
It a part of a sequence of honeycombs.
| [Order-7 tetrahedral honeycomb|] | [Order-7 cubic honeycomb|] | [Order-3-7 hexagonal honeycomb|] | [Order-3-7 heptagonal honeycomb|] | [Order-3-7 octagonal honeycomb|] | [Order-3-7 aperiogonal honeycomb|] | |
Order-8 dodecahedral honeycomb
In the geometry of hyperbolic 3-space, the order-8 dodecahedral honeycomb a regular space-filling tessellation. With Schläfli symbol, it has eight dodecahedra around each edge. All vertices are ultra-ideal with infinitely many dodecahedra existing around each vertex in an order-8 triangular tiling vertex arrangement.Poincaré disk model Cell-centered | Poincaré disk model |
It has a second construction as a uniform honeycomb, Schläfli symbol, 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. With Schläfli symbol. It has infinitely many dodecahedra around each edge. All vertices are ultra-ideal with infinitely many dodecahedra existing around each vertex in an infinite-order triangular tiling vertex arrangement.Poincaré disk model Cell-centered | Poincaré disk model | Ideal surface |
It has a second construction as a uniform honeycomb, Schläfli symbol, Coxeter diagram,, with alternating types or colors of dodecahedral cells.