Regular Pentagonal Tilings in Non-Euclidean Geometry
A dodecahedron can be considered a regular tiling of 12 pentagons on the surface of a sphere, with Schlafli symbol {5,3}, having 3 pentagons around reach vertex.
In the hyperbolic plane, there are tilings of regular pentagons, for instance order-4 pentagonal tiling, with Schlafli symbol {5,4}, having 4 pentagons around reach vertex. Higher order regular tilings {5,n} can be constructed on the hyperbolic plane, ending in {5,∞}.
| Sphere | Hyperbolic plane | |||||
|---|---|---|---|---|---|---|
{5,3} |
{5,4} |
{5,5} |
{5,6} |
{5,7} |
{5,8} |
...{5,∞} |
Read more about this topic: Pentagon Tiling
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