Tetraapeirogonal tiling
In geometry, the tetrapeirogonal tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of r{∞,4}.
Uniform constructions
There are 3 lower symmetry uniform construction, one with two colors of apeirogons, one with two colors of squares, and one with two colors of each:
Symmetry |
(*∞42) |
(*∞33) |
(*∞∞2) |
(*∞2∞2) |
|---|---|---|---|---|
Coxeter |
= |
= |
= {{CDD|labelinfin|branch_11|2a2b-cross|branch_11 |
|
Coloring |
Symmetry
The dual to this tiling represents the fundamental domains of *∞2∞2 symmetry group. The symmetry can be doubled by adding mirrors on either diagonal of the rhombic domains, creating *∞∞2 and *∞44 symmetry.
See also
- List of uniform planar tilings
- Tilings of regular polygons
- Uniform tilings in hyperbolic plane
References
- John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 19, "The Hyperbolic Archimedean Tessellations")