# Infinite-order triangular tiling

Infinite-order triangular tiling Poincaré disk model of the hyperbolic plane
Type Hyperbolic regular tiling
Vertex configuration 3
Schläfli symbol {3,∞}
Wythoff symbol ∞ | 3 2
Coxeter diagram         Symmetry group [∞,3], (*∞32)
Dual Order-3 apeirogonal tiling
Properties Vertex-transitive, edge-transitive, face-transitive

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.

## Symmetry

A lower symmetry form has alternating colors, and represented by cyclic symbol {(3,∞,3)},    . The tiling also represents the fundamental domains of the *∞∞∞ symmetry, 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 {3,p}.

### 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: 