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Lattices and packings in higher dimensions

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Abstract

A lattice in \(\mathbb{R}^3\) is a Λ that can be written as the set of integer combinations of three linearly independent vectors \(\{a,b,c\}\), say \(\Lambda= \mathbb{Z} \cdot a+\mathbb{Z} \cdot b+\mathbb{Z} \cdot c\). As in Sect. IX.4, two Euclidean invariants are immediately associated with a lattice; they are practically dictated when we seek to pack balls of like radius in the densest possible way, thus the most economical for practical life; see more in Sect. X.4.

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  1. Institut des Hautes Études Scientifiques, IHÉS, Bures-sur-Yvette, 35 route des Chartres, 91440, Bures-sur-Yvette, France

    Marcel Berger

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Berger, M. (2010). Lattices and packings in higher dimensions. In: Geometry Revealed. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70997-8_10

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