2021/05/04 by Dipendu Maity, Maity, Dipendu
Computer Science · Engineering · Materials Science · #Cellular Automata and Applications #Combinatorics (math.CO) #FOS: Mathematics #Quasicrystal Structures and Properties #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2105.01577
openalex publication_date 2021/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
If every vertex in a map has one out of two face-cycle types, then the map is said to be 2-semiequivelar. A 2-uniform tiling is an edge-to-edge tiling of regular polygons having 2 distinct transitivity classes of vertices. Clearly, a 2-uniform map is 2-semiequivelar. The converse of this is not true in general. There are 20 distinct 2-uniform tilings (these are of 14 different types) on the plane. In this article, we prove that a 2-semiequivelar toroidal map K has a finite 2-uniform cover if the universal cover of K is 2-uniform except of two types.