The raspberries in three dimensions with at most two sizes of berry
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915721517203456 |
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| author | Messerschmidt, Miek |
| author_facet | Messerschmidt, Miek |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_03408 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The raspberries in three dimensions with at most two sizes of berry Messerschmidt, Miek Metric Geometry Primary: 05B40. Secondary: 52C17 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. |
| title | The raspberries in three dimensions with at most two sizes of berry |
| topic | Metric Geometry Primary: 05B40. Secondary: 52C17 |
| url | https://arxiv.org/abs/2505.03408 |