Infinite-order apeirogonal tiling

Infinite-order apeirogonal tiling

Poincaré disk model of the hyperbolic plane
TypeHyperbolic regular tiling
Vertex figure
Schläfli symbol{,}
Wythoff symbol | 2
|
Coxeter diagram
Symmetry group[,], (*2)
[(,,)], (*)
Dualself-dual
PropertiesVertex-transitive, edge-transitive, face-transitive

In geometry, the infinite-order apeirogonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {∞,∞}, which means it has an infinite number of apeirogons around all its ideal vertices.

Symmetry

This tiling represents the fundamental domains of *∞ symmetry.

Uniform colorings

This tiling can also be alternately colored in the [(∞,∞,∞)] symmetry from 3 generator positions.

Domains 0 1 2

symmetry:
[(∞,∞,∞)]  

t0{(∞,∞,∞)}

t1{(∞,∞,∞)}

t2{(∞,∞,∞)}

Related polyhedra and tiling

The union of this tiling and its dual can be seen as orthogonal red and blue lines here, and combined define the lines of a *22 fundamental domain.

a{,} or =

See also

Wikimedia Commons has media related to Infinite-order apeirogonal tiling.

References

External links

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