Equivelar and d-Covered Triangulations of Surfaces. II. Cyclic Triangulations and Tessellations

TL;DR

This paper introduces a broad class of vertex-transitive cyclic triangulations of surfaces, including infinite series for various q-values, and derives related tessellations, expanding the understanding of surface triangulations.

Contribution

It presents new infinite series of cyclic q-equivelar triangulations for both orientable and non-orientable surfaces, and constructs related tessellations.

Findings

Infinite series of cyclic q-equivelar triangulations for q=3k and q=3k+1.

Construction of cyclic tessellations from these triangulations.

Applicability to both orientable and non-orientable surfaces.

Abstract

With the $[0,1,2]$-family of cyclic triangulations we introduce a rich class of vertex-transitive triangulations of surfaces. In particular, there are infinite series of cyclic $q$-equivelar triangulations of orientable and non-orientable surfaces for every $q=3k$, $k\geq 2$, and every $q=3k+1$, $k\geq 3$. Series of cyclic tessellations of surfaces are derived from these triangulated series.