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arXiv · 1401.2980

The local-global principle for integral bends in orthoplicial Apollonian sphere packings

Kei Nakamura
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Abstract

We introduce an orthoplicial Apollonian sphere packing, which is a sphere packing obtained by successively inverting a configuration of 8 spheres with 4-orthplicial tangency graph. We will show that there are such packings in which the bends of all constituent spheres are integral, and establish the asymptotic local-global principle for the set of bends in these packings.

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Kei Nakamura. 2014-01-13. The local-global principle for integral bends in orthoplicial Apollonian sphere packings. https://arxiv.org/abs/1401.2980

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