### Abstract

Given a simple polygon in the plane, a deflation is defined as the inverse of a flip in the Erdos-Nagy sense. In 1993 Bernd Wegner conjectured that every simple polygon admits only a finite number of deflations. In this note we describe a counterexample to this conjecture by exhibiting a family of polygons on which deflations go on forever.

Original language | English (US) |
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Pages (from-to) | 307-311 |

Number of pages | 5 |

Journal | Beitrage zur Algebra und Geometrie |

Volume | 42 |

Issue number | 2 |

State | Published - 2001 |

### ASJC Scopus subject areas

- Algebra and Number Theory
- Geometry and Topology

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## Cite this

Fevens, T., Hernandez, A., Mesa, A., Morin, P., Soss, M., & Toussaint, G. (2001). Simple polygons with an infinite sequence of deflations.

*Beitrage zur Algebra und Geometrie*,*42*(2), 307-311.