Locally equiangular triangulations

Abstract

Lawson (1972) has given a criterion of local equiangularity of a triangulation of the convex hull of a finite set of distinct points in the plane. In this note it is shown that (with suitable modifications to deal with degeneracy) there is only one such triangulation, and that it is the Delaunay triangulation (Rogers, 1964). 10.1093/comjnl/21.3.243