Compact packings of space with two sizes of spheres. (English) Zbl 1462.52029
Summary: Compact sphere packings are sphere packings which can be seen as tilings. They are usually good candidates to maximize the density. We show that the compact packings of Euclidean three-dimensional space with two sizes of spheres are exactly those obtained by filling with spheres of size \(\sqrt{2} - 1\) the octahedral holes of a close-packing of spheres of size 1.
MSC:
| 52C17 | Packing and covering in \(n\) dimensions (aspects of discrete geometry) |
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