# Point-ellipse and some other exotic configurations

## TL;DR

This paper introduces point-ellipse and point-conic configurations, exploring their properties and presenting two families of balanced configurations, one based on Carnot's theorem and the other on Cartesian products of polygons, including a configuration related to the 24-cell.

## Contribution

It is the first to define and analyze point-ellipse and point-conic configurations, providing new constructions and insights into their properties.

## Key findings

- Two families of balanced point-ellipse and point-conic configurations are described.
- Construction methods include Carnot's theorem and Cartesian products of polygons.
- A specific configuration based on the regular 24-cell is investigated.

## Abstract

In this paper we introduce point-ellipse configurations and point-conic configurations. We study some of their basic properties and describe two interesting families of balanced point-ellipse, respectively point-conic $6$-configurations. The construction of the first family is based on Carnot's theorem, whilst the construction of the second family is based on the Cartesian product of two regular polygons. Finally, we investigate a point-ellipse configuration based on the regular $24$-cell.