The growing ratios of hyperbolic regular mosaics with bounded cells

TL;DR

This paper calculates the growth ratios of hyperbolic regular mosaics with bounded cells in 3- and 4-dimensional spaces by iteratively constructing belts around vertices.

Contribution

It provides a generalized method to determine the growing ratios for all such hyperbolic mosaics, expanding understanding of their geometric properties.

Findings

Calculated growth ratios for all 3D hyperbolic mosaics with bounded cells.

Extended the analysis to 4D hyperbolic mosaics.

Established a generalized approach for these calculations.

Abstract

In 3- and 4-dimensional hyperbolic spaces there are four, respectively five, regular mosaics with bounded cells. A belt can be created around an arbitrary base vertex of a mosaic. The construction can be iterated and a growing ratio can be determined by using the number of the cells of the considered belts. In this article we determine these growing ratios for each mosaic in a generalized way.