Coordinates for a new triangular tiling of the hyperbolic plane

TL;DR

This paper introduces a new family of triangular tilings for the hyperbolic plane, providing a systematic coordinate system for locating individual triangles within these tilings.

Contribution

It defines an infinite family of hyperbolic triangular tilings parameterized by two natural numbers and establishes a uniform coordinate system for their triangles.

Findings

Defined an infinite family of hyperbolic triangular tilings.

Developed a uniform coordinate system for the tilings.

Provided a mathematical framework for locating triangles.

Abstract

In this paper we define an infinite family of triangular tilings of the hyperbolic plane defined by two parameters ranging in the natural nummbers and we give a uniform way to define coordinates for locating the triangles of the tiling.