### Abstract

The vertices of a convex planar nonagon determine exactly five distances if and only if they are nine vertices of a regular 10-gon or a regular 11-gon. This result has important ties to related concerns, including the maximum number of points in the plane that determine exactly five distances and, for each n ≥ 7, the smallest t for which there exists a convex n-gon whose vertices determine t distances and are not all on one circle.

Original language | English |
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Pages (from-to) | 317-332 |

Number of pages | 16 |

Journal | Geometriae Dedicata |

Volume | 60 |

Issue number | 3 |

Publication status | Published - Dec 1 1996 |

### Keywords

- Convex nonagons
- Erdös conjecture
- Intervertex distances
- Lattice theory

### ASJC Scopus subject areas

- Geometry and Topology

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## Cite this

Erdös, P., & Fishburn, P. (1996). Convex nonagons with five intervertex distances.

*Geometriae Dedicata*,*60*(3), 317-332.