The local-global principle for integral bends in orthoplicial Apollonian   sphere packings
  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. 
Kei Nakamura
math.NT math.GR math.MG