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

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 $q=3k$, $k\ge 2$, and every $q=3k+1$, $k\ge 3$. Series of cyclic tessellations of surfaces are derived from these triangulated series.

27 pages, 18 figures

References in corpus (4)

• Surface realization with the intersection edge functional
• Triangulated Manifolds with Few Vertices: Vertex-Transitive Triangulations I
• A note on the existence of {k, k}-equivelar polyhedral maps
• Equivelar and d-Covered Triangulations of Surfaces. I

Cited by in corpus (4)

• Partitioning the triangles of the cross polytope into surfaces
• Equivelar and d-Covered Triangulations of Surfaces. I
• Combinatorial 3-manifolds with transitive cyclic symmetry
• Combinatorial Seifert fibred spaces with transitive cyclic automorphism group