The raspberries in three dimensions with at most two sizes of berry

2025/05/06 by Messerschmidt, Miek
#FOS: Mathematics #Metric Geometry (math.MG) #Primary: 05B40. Secondary: 52C17

paper · doi:10.48550/arxiv.2505.03408

Abstract

In three dimensional Euclidean space, a raspberry is defined to be an arrangement of spheres with pairwise disjoint interiors, where all spheres are tangent to a central unit sphere and such that the contact graph of the non-central spheres triangulates the central sphere. We discuss the relevance of these structures in related 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.

Citations

• On compact packings of Euclidean space with spheres of finitely many sizes
• Rigidity, Tensegrity and Reconstruction of Polytopes under Metric Constraints
• Compact packings of space with three sizes of spheres
• Compact packings of the space with two sizes of spheres

Related

• Sphere packings II
• On the configurations of four spheres supporting the vertices of a tetrahedron
• Compact packings of space with three sizes of spheres
• Complementary bodies in sphere packing
• On integer radii coin representations of the wheel graph