2014/01/13 by Nakamura, Kei
#11D85 #11E39 #11F06 #20H05 #52C17 #FOS: Mathematics #Group Theory (math.GR) #Metric Geometry (math.MG) #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1401.2980
We introduce an orthoplicial Apollonian sphere packing, which is a sphere packing obtained by successively inverting a configuration of 8 spheres with 4-orthplicial tangency graph. We will show that there are such packings in which the bends of all constituent spheres are integral, and establish the asymptotic local-global principle for the set of bends in these packings.