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.

The regular map {8,3}_2,0 can be seen as a 6-coloring of the {8,3} hyperbolic tiling. Within the regular map, octagons of the same color are considered the same face shown in multiple locations. The 2,0 subscripts show the same color will repeat by moving 2 steps in a straight direction following opposite edges. This regular map also has a representation as a double covering of a cube, represented by Schläfli symbol {8/2,3}, with 6 octagonal faces, double wrapped {8/2}, with 24 edges, and 16 vertices. It was described by Branko Grünbaum in his 2003 paper Are Your Polyhedra the Same as My Polyhedra?^[1]

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.

• Tilings of regular polygons
• List of uniform planar tilings
• List of regular polytopes

• Weisstein, Eric W. "Hyperbolic tiling". MathWorld.
• Weisstein, Eric W. "Poincaré hyperbolic disk". MathWorld.
• Hyperbolic and Spherical Tiling Gallery
• KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings
• Hyperbolic Planar Tessellations, Don Hatch