Apollonian Circle Packings: Geometry and Group Theory III. Higher Dimensions

This paper gives n-dimensional analogues of the Apollonian circle packings in Parts I and II. Those papers considered circle packings described in terms of their Descartes configurations, which are sets of four mutually touching circles. They studied packings that had integrality properties in terms of the curvatures and centers of the circles. Here we consider collections of n-dimensional Descartes configurations, which consist of n + 2 mutually touching spheres. We work in the space Mn D of all n-dimensional oriented Descartes configurations parametrized in a coordinate system, augmented curvature-center coordinates, as those (n + 2)

• Type: Journal
• Year: 2006
• Where: DCG
• Authors: Ronald L. Graham, Jeffrey C. Lagarias, Colin L. Mallows, Allan R. Wilks, Catherine H. Yan
• Keywords: Circle Packings, DCG 2006, Descartes Configurations, N-dimensional