The Local-Global Principle for Integral Generalized Apollonian Sphere Packings

2014/01/20 by Dimitri Dias, Dias, Dimitri · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematics and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1401.4789

openalex publication_date 2014/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Four mutually tangent spheres form two gaps. In each of these, one can inscribe in a unique way four mutually tangent spheres such that each one of these spheres is tangent to exactly three of the original spheres. Repeating the process gives rise to a generalized Apollonian sphere packing. These packings have remarkable properties. One of them is the local to global principle and will be proven in this paper.

Cited by

• Asymptotic Density of Apollonian-Type Packings

Related

• The local-global principle for integral bends in orthoplicial Apollonian sphere packings
• On the Local-Global Principle for Integral Apollonian-3 Circle Packings
• The Local-Global Principle for Integral Soddy Sphere Packings
• Apollonian packings in seven and eight dimensions
• The Local-Global Conjecture is False for Generalized Circle Packings