# The polycons: the sphericon (or tetracon) has found its family

## TL;DR

This paper introduces a new family of developable solids called polycons, generalizing the sphericon, and explores their static and rolling properties, comparing them to similar shapes and discussing their artistic aspects.

## Contribution

The paper presents the polycons as a novel family of shapes extending the sphericon, with detailed analysis of their properties and behaviors.

## Key findings

- Polycons generalize the sphericon family.
- Polycons exhibit unique rolling behaviors.
- Comparison with oloid and polysphericons highlights differences.

## Abstract

This paper introduces a new family of solids, which we call \textit{polycons}, which generalise the sphericon in a natural way. The static properties of the polycons are derived, and their rolling behaviour is described and compared to that of other developable rollers such as the oloid and particular polysphericons. The paper concludes with a discussion of the polycons as stationary and kinetic works of art.