Heptagonal tiling honeycomb


In the geometry of hyperbolic 3-space, the heptagonal tiling honeycomb or 7,3,3 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 heptagonal tiling honeycomb is, with three heptagonal tilings meeting at each edge. The vertex figure of this honeycomb is a tetrahedron,.

Poincaré disk model

Rotating
Ideal surface

Related polytopes and honeycombs

It is a part of a series of regular polytopes and honeycombs with Schläfli symbol, and tetrahedral vertex figures:
It is a part of a series of regular honeycombs,.
Order-3-4 heptagonal honeycomb|Order-3-5 heptagonal honeycomb|Order-3-6 heptagonal honeycomb|Order-3-7 heptagonal honeycomb|Order-3-8 heptagonal honeycomb|...Order-3-infinite heptagonal honeycomb|

It is a part of a series of regular honeycombs, with.
Order-4-3 heptagonal honeycomb|Order-5-3 heptagonal honeycomb|...

Octagonal tiling honeycomb

In the geometry of hyperbolic 3-space, the octagonal tiling honeycomb or 8,3,3 honeycomb a regular space-filling tessellation. Each infinite cell consists of an 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 octagonal tiling honeycomb is, with three octagonal tilings meeting at each edge. The vertex figure of this honeycomb is an tetrahedron,.

Poincaré disk model
Direct subgroups of

Apeirogonal tiling honeycomb

In the geometry of hyperbolic 3-space, the apeirogonal tiling honeycomb or ∞,3,3 honeycomb a regular space-filling tessellation. Each infinite cell consists of an 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 apeirogonal tilings meeting at each edge. The vertex figure of this honeycomb is an tetrahedron,.
The "ideal surface" projection below is a plane-at-infinity, in the Poincare half-space model of H3. It shows an Apollonian gasket pattern of circles inside a largest circle.

Poincaré disk model
Ideal surface