The growing ratios of hyperbolic regular mosaics with bounded cells

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The growing ratios of hyperbolic regular mosaics with bounded cells L ́aszl ́o N ́emeth

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.

DOI: https://armjmath.sci.am/index.php/ajm/article/view/142 Armenian Journal of Mathematics, 9(1) 1-19

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Keywords

hyperbolic mosaic, regular mosaic, regular tessalation, honey-comb

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