Trioctagonal tiling
In geometry, the trioctagonal tiling is a semiregular tiling of the hyperbolic plane, representing a rectified Order-3 octagonal tiling. There are two triangles and two octagons alternating on each vertex. It has Schläfli symbol of r.
Symmetry
The half symmetry = can be shown with alternating two colors of triangles, by Coxeter diagram. | Dual tiling |
Related polyhedra and tilings
From a Wythoff construction there are eight 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 8 forms.
It can also be generated from the hyperbolic tilings:
The trioctagonal tiling can be seen in a sequence of quasiregular polyhedrons and tilings: