Convex nonagons with five intervertex distances

Paul Erdös, Peter Fishburn

Research output: Article

8 Citations (Scopus)


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 languageEnglish
Pages (from-to)317-332
Number of pages16
JournalGeometriae Dedicata
Issue number3
Publication statusPublished - 1996

ASJC Scopus subject areas

  • Geometry and Topology

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