Truncated triapeirogonal tiling

In geometry, the truncated triapeirogonal tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of tr.

Symmetry

The dual of this tiling represents the fundamental domains of , *∞32 symmetry. There are 3 small index subgroup constructed from 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 special index 4 reflective subgroup, is,, and its direct subgroup ⁺,, and semidirect subgroup,. Given with generating mirrors, then its index 4 subgroup has generators.
An index 6 subgroup constructed as, becomes,.

Related polyhedra and tiling

This tiling can be considered a member of a sequence of uniform patterns with vertex figure and Coxeter-Dynkin diagram. For p < 6, the members of the sequence are omnitruncated polyhedra, shown below as spherical tilings. For p >; 6, they are tilings of the hyperbolic plane, starting with the truncated triheptagonal tiling.