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<p>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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月29日

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  • Miek Messerschmidt

摘要

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.