Rhombihexaoctagonal tiling

Rhombihexaoctagonal tiling

Poincaré disk model of the hyperbolic plane
TypeHyperbolic uniform tiling
Vertex configuration6.4.8.4
Schläfli symbolrr{8,6}
Wythoff symbol6 | 8 2
Coxeter diagram
Symmetry group[8,6], (*862)
DualDeltoidal hexaoctagonal tiling
PropertiesVertex-transitive

In geometry, the rhombihexaoctagonal tiling is a semiregular tiling of the hyperbolic plane. It has Schläfli symbol of rr{8,6}.

Symmetry

The dual tiling, called a deltoidal hexaoctagonal tiling represent the fundamental domains of *4232 symmetry, a half symmetry of [8,6], (*862) as [8,1+,6].

Related polyhedra and tilings

From a Wythoff construction there are fourteen hyperbolic uniform tilings that can be based from the regular order-6 octagonal tiling.

Drawing the tiles colored as red on the original faces, yellow at the original vertices, and blue along the original edges, there are 7 forms with full [8,6] symmetry, and 7 with subsymmetry.

See also

Wikimedia Commons has media related to Uniform tiling 4-6-4-8.

References

External links

This article is issued from Wikipedia - version of the Tuesday, November 11, 2014. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.