Order-3-6 heptagonal honeycomb
In the geometry of hyperbolic 3-space, the order-3-6 heptagonal honeycomb a regular space-filling tessellation. Each infinite cell consists of a heptagonal 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-3-6 heptagonal honeycomb is, with six heptagonal tilings meeting at each edge. The vertex figure of this honeycomb is a triangular tiling,.It has a quasiregular construction,, which can be seen as alternately colored cells.
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 triangular tiling vertex figures.Order-3-6 octagonal honeycomb
In the geometry of hyperbolic 3-space, the order-3-6 octagonal honeycomb a regular space-filling tessellation. Each infinite cell consists of an order-6 octagonal tiling whose vertices lie on a 2-hypercycle, each of which has a limiting circle on the ideal sphere.The Schläfli symbol of the order-3-6 octagonal honeycomb is, with six octagonal tilings meeting at each edge. The vertex figure of this honeycomb is a triangular tiling,.
It has a quasiregular construction,, which can be seen as alternately colored cells.
Poincaré disk model |
Order-3-6 apeirogonal honeycomb
In the geometry of hyperbolic 3-space, the order-3-6 apeirogonal honeycomb a regular space-filling tessellation. Each infinite cell consists of an order-3 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 order-3-6 apeirogonal honeycomb is, with six order-3 apeirogonal tilings meeting at each edge. The vertex figure of this honeycomb is a triangular tiling,.
Poincaré disk model | Ideal surface |
It has a quasiregular construction,, which can be seen as alternately colored cells.