Analogs of Steiner's porism and Soddy's hexlet in higher dimensions via spherical codes

TL;DR

This paper explores higher-dimensional generalizations of classical tangent sphere chain results, extending Steiner's porism and Soddy's hexlet concepts through the use of spherical codes.

Contribution

It introduces novel higher-dimensional analogs of classical tangent sphere configurations using spherical codes, expanding the geometric understanding beyond traditional 3D cases.

Findings

Established higher-dimensional Steiner's porism analogs

Developed Soddy's hexlet generalizations in higher dimensions

Connected spherical codes with tangent sphere configurations

Abstract

In this paper we consider generalizations of classical results on chains of tangent spheres to higher dimensions.