# Self-similar shapes under Errera division rule on the cone

## TL;DR

This paper introduces a method to construct cell shapes invariant under the Errera division rule on conical surfaces, analyzing how tissue curvature affects cell division patterns and providing bounds for biologically relevant cone angles.

## Contribution

It presents a novel construction method for invariant cell shapes under Errera division on cones and analyzes the influence of tissue curvature on division rules.

## Key findings

- Cell shape invariance under Errera rule on cones
- Analytical bounds for cone apical angles
- Curvature influences division patterns

## Abstract

This study provides a general construction method of cell shape invariant by the Errera rule of division on a cone and provides analytical bounds for the apical angle of the cone on which these cells are connected and thus biologically meaningful. This idealized model highlights how the curvature of the tissue can influence Errera rule.