In geometry, the truncated tetrapentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t0,1,2{4,5} or tr{4,5}.
Symmetry
There are four small index subgroup constructed from [5,4] by mirror removal and alternation. In these images fundamental domains are alternately colored black and white, and mirrors exist on the boundaries between colors.
A radical subgroup is constructed [5*,4], index 10, as [5+,4], (5*2) with gyration points removed, becoming orbifold (*22222), and its direct subgroup [5*,4]+, index 20, becomes orbifold (22222). Small index subgroups of [5,4]Index1210DiagramCoxeter(orbifold)[5,4] = (*542)[5,4,1+] = = (*552)[5+,4] = (5*2)[5*,4] = (*22222)Direct subgroupsIndex2420DiagramCoxeter(orbifold)[5,4]+ = (542)[5+,4]+ = = (552)[5*,4]+ = (22222)
Related polyhedra and tiling
See also
Uniform tilings in hyperbolic plane List of regular polytopes
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