In geometry, the truncated order-8 triangular tiling is a semiregular tiling of the hyperbolic plane. There are two hexagons and one octagon on each vertex. It has Schläfli symbol of t{3,8}.
Uniform colors
The half symmetry [1+,8,3] = [(4,3,3)] can be shown with alternating two colors of hexagonsDual tiling
Symmetry The dual of this tiling represents the fundamental domains of *443 symmetry. It only has one subgroup 443, replacing mirrors with gyration points.
This symmetry can be doubled to 832 symmetry by adding a bisecting mirror to the fundamental domain. + Small index subgroups of [(4,3,3)], (*433)TypeReflectional RotationalIndex12DiagramCoxeter(orbifold)[(4,3,3)] = (*433)[(4,3,3)]+ = (433)
Related tilings From a Wythoff construction there are ten hyperbolic uniform tilings that can be based from the regular octagonal tiling.
It can also be generated from the (4 3 3) hyperbolic tilings:
This hyperbolic tiling is topologically related as a part of sequence of uniform truncated polyhedra with vertex configurations (n.6.6), and [n,3] Coxeter group symmetry.
See also
Triangular tiling Order-3 octagonal tiling Order-8 triangular tiling Tilings of regular polygons List of uniform tilings
References
John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, (Chapter 19, The Hyperbolic Archimedean Tessellations)
External links
Hyperbolic and Spherical Tiling Gallery KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings Hyperbolic Planar Tessellations, Don Hatch