Truncated triheptagonal tiling


In geometry, the truncated triheptagonal tiling is a semiregular tiling of the hyperbolic plane. There are one square, one hexagon, and one tetradecagon on each vertex. It has Schläfli symbol of tr.

Uniform colorings

There is only one uniform coloring of a truncated triheptagonal tiling.

Symmetry

Each triangle in this dual tiling, order 3-7 kisrhombille, represent a fundamental domain of the Wythoff construction for the symmetry group .

Related polyhedra and tilings

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.
From a Wythoff construction there are eight hyperbolic uniform tilings that can be based from the regular heptagonal tiling.
Drawing the tiles colored as red on the original faces, yellow at the original vertices, and blue along the original edges, there are 8 forms.