Infinite-order triangular tiling explained

In geometry, the infinite-order triangular tiling is a regular tiling of the hyperbolic plane with a Schläfli symbol of . All vertices are ideal, located at "infinity" and seen on the boundary of the Poincaré hyperbolic disk projection.

Symmetry

A lower symmetry form has alternating colors, and represented by cyclic symbol, . The tiling also represents the fundamental domains of the

, which can be seen with 3 colors of lines representing 3 mirrors of the construction.

Related polyhedra and tiling

This tiling is topologically related as part of a sequence of regular polyhedra with Schläfli symbol .

Other infinite-order triangular tilings

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

See also

References