Top Qs
Timeline
Chat
Perspective

Infinite-order square tiling

From Wikipedia, the free encyclopedia

Infinite-order square tiling
Remove ads

In geometry, the infinite-order square tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {4,∞}. All vertices are ideal, located at "infinity", seen on the boundary of the Poincaré hyperbolic disk projection.

Infinite-order square tiling
Thumb
Poincaré disk model of the hyperbolic plane
TypeHyperbolic regular tiling
Vertex configuration4
Schläfli symbol{4,}
Wythoff symbol | 4 2
Coxeter diagram
Symmetry group[,4], (*42)
DualOrder-4 apeirogonal tiling
PropertiesVertex-transitive, edge-transitive, face-transitive
Remove ads

Uniform colorings

There is a half symmetry form, , seen with alternating colors:

Thumb

Symmetry

This tiling represents the mirror lines of *∞∞∞∞ symmetry. The dual to this tiling defines the fundamental domains of (*2) orbifold symmetry.

Thumb

This tiling is topologically related as a part of sequence of regular polyhedra and tilings with vertex figure (4n).

More information Spherical, Euclidean ...
More information Dual figures, Alternations ...

See also

References

Loading content...
Loading related searches...

Wikiwand - on

Seamless Wikipedia browsing. On steroids.

Remove ads