Enriques surfaces and an Apollonian packing in eight dimensions

Abstract We call a packing of hyperspheres in n dimensions an Apollonian sphere if the spheres intersect tangentially or not at all; they fill -dimensional Euclidean space; and every is member cluster $n+2$ mutually tangent (and few more properties described herein). In this paper, we describe eight that naturally arises from study generic nodal Enriques surfaces. The $E_7$ , $E_8$ Reye lattices play roles. use to generate nine dimensions, cross section seven weakly Apollonian. Maxwell all three packings but seemed unaware are different than those found earlier paper. passing, give sufficient condition for Coxeter graph identify Soddy packing.