2010/10/29 by Aldo-Hilario Cruz-Cota, Cruz-Cota, Aldo-Hilario
Mathematics · #57M15 #57M50 #FOS: Mathematics #Geometric Topology (math.GT) #Metric Geometry (math.MG) #math.GT #math.MG #msc:57M15 #msc:57M50
paper · pdf · doi:10.48550/arxiv.1010.6236
14 pages, 9 figures
arxiv created 2010/10/29 · arxiv updated 2010/11/01
A hex sphere is a singular Euclidean sphere with four cones points whose cone angles are (integer) multiples of 2*pi/3 but less than 2*pi. Given a hex sphere M, we consider its Voronoi decomposition centered at the two cone points with greatest cone angles. In this paper we use elementary Euclidean geometry to describe the Voronoi regions of hex spheres and classify the Voronoi graphs of hex spheres (up to graph isomorphism).