Infinite-order triangular tiling

In geometry, the infinite-order triangular tiling is a regular tiling of the hyperbolic plane with a Schläfli symbol of {3,∞}.

All vertices are ideal, located at "infinity" and seen on the boundary of the Poincaré hyperbolic disk projection.

A lower symmetry form has alternating colors, and represented by cyclic symbol {(3,∞,3)}, .

This tiling is topologically related as part of a sequence of regular polyhedra with Schläfli symbol {3,p}.

A nonregular infinite-order triangular tiling can be generated by a recursive process from a central triangle as shown here:

The {3,3,∞} honeycomb has {3,∞} vertex figures.