The Raspberries in Three Dimensions with at Most Two Sizes of Berry

Abstract In three dimensional Euclidean space, a raspberry is defined to be an arrangement of spheres with pairwise disjoint interiors, so that all spheres are tangent to a central unit sphere and is such that the contact graph of the non-central spheres triangulate the central sphere. We discuss the relevance of these structures in other work. We present a catalog of all configurations of radii that permit the formation of raspberries that have at most two sizes of non-central spheres. Throughout we discuss the construction of this catalog.