Order-3-6 heptagonal honeycomb

In the geometry of hyperbolic 3-space, the order-3-6 heptagonal honeycomb a regular space-filling tessellation (or honeycomb). 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 {7,3,6}, with six heptagonal tilings meeting at each edge. The vertex figure of this honeycomb is an triangular tiling, {3,6}.

It has a quasiregular construction,, which can be seen as alternately colored cells.

Related polytopes and honeycombs
It is a part of a series of regular polytopes and honeycombs with {p,3,6} 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 (or honeycomb). 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 {8,3,6}, with six octagonal tilings meeting at each edge. The vertex figure of this honeycomb is a triangular tiling, {3,6}.

It has a quasiregular construction,, which can be seen as alternately colored cells.

Order-3-6 apeirogonal honeycomb
In the geometry of hyperbolic 3-space, the order-3-6 apeirogonal honeycomb a regular space-filling tessellation (or honeycomb). 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 {∞,3,6}, with six order-3 apeirogonal tilings meeting at each edge. The vertex figure of this honeycomb is a triangular tiling, {3,6}.

It has a quasiregular construction,, which can be seen as alternately colored cells.