Order-7 hexagonal tiling honeycomb

Order-7 hexagonal tiling honeycomb

Rendered intersection of honeycomb with the ideal plane in Poincaré half-space model
TypeHyperbolic regular honeycomb
Schläfli symbol{6,3,7}
Coxeter diagrams
Cells{6,3}
Faces{6}
Edge figure{7}
Vertex figure{3,8}
Dual{7,3,6}
Coxeter group[6,3,7]
PropertiesRegular

In the geometry of hyperbolic 3-space, the order-7 hexagonal tiling honeycomb a regular space-filling tessellation (or honeycomb) with Schläfli symbol {6,3,7}.

Geometry

All vertices are ultra-ideal (existing beyond the ideal boundary) with seven hexagonal tilings existing around each edge and with an order-7 triangular tiling vertex figure.


Closeup

Related polytopes and honeycombs

It a part of a sequence of regular polychora and honeycombs with hexagonal tiling cells.

Infinite-order hexagonal tiling honeycomb

Infinite-order hexagonal tiling honeycomb

Rendered intersection of honeycomb with the ideal plane in Poincaré half-space model
TypeHyperbolic regular honeycomb
Schläfli symbols{6,3,∞}
{6,(3,∞,3)}
Coxeter diagrams
↔
↔
Cells{6,3}
Faces{6}
Edge figure{∞}
Vertex figure{3,∞}, {(3,∞,3)}
Dual{∞,3,6}
Coxeter group[6,3,∞]
[6,((3,∞,3))]
PropertiesRegular

In the geometry of hyperbolic 3-space, the infinite-order hexagonal tiling honeycomb is a regular space-filling tessellation (or honeycomb) with Schläfli symbol {6,3,∞}. It has infinitely many hexagonal tiling {6,3} around each edge. All vertices are ultra-ideal (Existing beyond the ideal boundary) with infinitely many hexagonal tilings existing around each vertex in an infinite-order triangular tiling vertex arrangement.

Symmetry constructions

It has a second construction as a uniform honeycomb, Schläfli symbol {6,(3,∞,3)}, Coxeter diagram, , with alternating types or colors of hexagonal tiling cells.

See also

References

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