In geometry, the truncated order-4 pentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t0,1{5,4}.
Uniform colorings A half symmetry [1+,4,5] = [5,5] coloring can be constructed with two colors of decagons. This coloring is called a truncated pentapentagonal tiling.
Symmetry There is only one subgroup of [5,5], [5,5]+, removing all the mirrors. This symmetry can be doubled to 542 symmetry by adding a bisecting mirror. + Small index subgroups of [5,5]TypeReflective domainsRotational symmetryIndex12DiagramCoxeter(orbifold)[5,5] = = (*552)[5,5]+ = = (552)
Related polyhedra and tiling
References John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, (Chapter 19, The Hyperbolic Archimedean Tessellations)
See also
Uniform tilings in hyperbolic plane 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