Tetrapentagonal tiling

In geometry, the tetrapentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t₁{4,5} or r{4,5}.

Symmetry

A half symmetry [1⁺,4,5] = [5,5] construction exists, which can be seen as two colors of pentagons. This coloring can be called a rhombipentapentagonal tiling.

Dual tiling

The dual tiling is made of rhombic faces and has a face configuration V4.5.4.5:

Related polyhedra and tiling

See also

• Binary tiling, an aperiodic tiling of the hyperbolic plane by pentagons
• Uniform tilings in hyperbolic plane
• List of regular polytopes

References

• John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, (Chapter 19, The Hyperbolic Archimedean Tessellations)

External links

• Hyperbolic and Spherical Tiling Gallery
• KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
• Hyperbolic Planar Tessellations, Don Hatch