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Analogs of Steiner’s porism and Soddy’s hexlet in higher dimensions via spherical codes. (English) Zbl 1406.52038

The paper under review deals with configurations of spheres in \(\mathbb R^n\) and provides a clever method for deriving far-reaching multidimensional generalizations of classical results concerning Steiner’s porism in \(\mathbb R^2\) and Soddy’s hexlet in \(\mathbb R^3\). The construction is based on the use of kissing arrangements of spheres in \(\mathbb R^n\), spherical packings and spherical codes.

MSC:

52C17 Packing and covering in \(n\) dimensions (aspects of discrete geometry)
52C26 Circle packings and discrete conformal geometry
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