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

2010/01/15 by Lutz, Frank H.
#52B05 #52B70 #52C20 #57Q15 #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1001.2779

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

Related

• Equivelar and d-Covered Triangulations of Surfaces. I
• Tessellations of surfaces
• Irreducible triangulations of low genus surfaces
• Ideally, all infinite type surfaces can be triangulated
• Degree-regular triangulations of surfaces