Order-4-4 pentagonal honeycomb
In the geometry of hyperbolic 3-space, the order-4-4 pentagonal honeycomb a regular space-filling tessellation. Each infinite cell consists of a pentagonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere.
Geometry
The Schläfli symbol of the order-4-4 pentagonal honeycomb is, with four order-4 pentagonal tilings meeting at each edge. The vertex figure of this honeycomb is a square tiling,.Poincaré disk model | Ideal surface |
Related polytopes and honeycombs
It is a part of a series of regular polytopes and honeycombs with Schläfli symbol, and square tiling vertex figures:Order-4-4 hexagonal honeycomb
In the geometry of hyperbolic 3-space, the order-4-4 hexagonal honeycomb a regular space-filling tessellation. Each infinite cell consists of an order-4 hexagonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere.The Schläfli symbol of the octagonal tiling honeycomb is, with three octagonal tilings meeting at each edge. The vertex figure of this honeycomb is a square tiling,.
Poincaré disk model | Ideal surface |
Order-4-4 apeirogonal honeycomb
In the geometry of hyperbolic 3-space, the order-4-4 apeirogonal honeycomb a regular space-filling tessellation. Each infinite cell consists of an order-4 apeirogonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere.The Schläfli symbol of the apeirogonal tiling honeycomb is, with three order-4 apeirogonal tilings meeting at each edge. The vertex figure of this honeycomb is a square tiling,.
Poincaré disk model | Ideal surface |