Modified contact simplex iteration

TL;DR

This paper investigates the iterative process of contact simplexes, introducing the concept of a root of a simplex, and demonstrates the existence of two partial limits in the circumcenter sequence of these iterated simplexes.

Contribution

It introduces the concept of the root of a simplex and analyzes the limiting behavior of circumcenters under iterative contact simplex procedures.

Findings

The root of a simplex is defined as a homothety image with a specific coefficient.

The circumcenter sequence of iterated root simplexes has two partial limits.

The study provides new insights into the geometric properties of contact simplexes.

Abstract

We study the iterations of the procedure of taking the contact simplex. We define the concept of the root of the simplex, which is a homothety image of contact simplex with a special coefficient greater than 1. The article shows that once we iterate the root of a given simplex, the circumcenter sequence of these simplices has two partial limits.