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We introduce an orthoplicial Apollonian sphere packing, which is a spherepacking obtained by successively inverting a configuration of 8 spheres with4-orthplicial tangency graph. We will show that there are such packings inwhich the bends of all constituent spheres are integral, and establish theasymptotic local-global principle for the set of bends in these packings.

The local-global principle for integral bends in orthoplicial Apollonian sphere packings