Ma-Schlenker c-Octahedra in the 2-Sphere

TL;DR

This paper demonstrates the non-rigidity of spherical inversive distance circle packings through elementary constructions based solely on the inversive geometry of the 2-sphere, inspired by Ma-Schlenker examples.

Contribution

It introduces new elementary constructions that show non-rigidity of spherical circle packings, avoiding complex tools used in prior work.

Findings

Spherical inversive distance circle packings are non-rigid.

Elementary constructions can demonstrate non-rigidity.

Provides alternative methods inspired by Ma-Schlenker examples.

Abstract

We present constructions inspired by the Ma-Schlenker example of~\cite{Ma:2012hl} that show the non-rigidity of spherical inversive distance circle packings. In contrast to the use in~\cite{Ma:2012hl} of an infinitesimally flexible Euclidean polyhedron, embeddings in de Sitter space, and Pogorelov maps, our elementary constructions use only the inversive geometry of the $2$-sphere.