In geometry, the truncated order-6 pentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t1,2{6,5}.
Uniform colorings
t012(5,5,3)With mirrors An alternate construction exists from the [(5,5,3)] family, as the omnitruncation t012(5,5,3). It is shown with two (colors) of decagons.
Symmetry The dual of this tiling represents the fundamental domains of the *553 symmetry. There are no mirror removal subgroups of [(5,5,3)], but this symmetry group can be doubled to 652 symmetry by adding a bisecting mirror to the fundamental domains. + Small index subgroups of [(5,5,3)]TypeReflective domainsRotational symmetryIndex12DiagramCoxeter(orbifold)[(5,5,3)] = (*553)[(5,5,3)]+ = (553)
Related polyhedra and tiling
+ [(5,5,3)] reflective symmetry uniform tilings
References John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, (Chapter 19, The Hyperbolic Archimedean Tessellations)
See also
Square tiling Tilings of regular polygons List of uniform planar tilings List of regular polytopes
External links
Hyperbolic and Spherical Tiling Gallery KaleidoTile 3: Educational software to create spherical, planar and hyperbolic tilings Hyperbolic Planar Tessellations, Don Hatch