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In geometry, the octagonal tiling is a regular tiling of the hyperbolic plane. It is represented by Schläfli symbol of {8,3}, having three regular octagons around each vertex.
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Uniform colorings
Like the hexagonal tiling of the Euclidean plane, there are 3 uniform colorings of this hyperbolic tiling. The dual tiling V8.8.8 represents the fundamental domains of [(4,4,4)] symmetry.
Related polyhedra and tilings
This tiling is topologically part of sequence of regular polyhedra and tilings with Schläfli symbol {n,3}.
And also is topologically part of sequence of regular tilings with Schläfli symbol {8,n}.
From a Wythoff construction there are ten hyperbolic uniform tilings that can be based from the regular 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 10 forms.