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arXiv · 1910.00629

Uniqueness of Optimal Point Sets Determining Two Distinct Triangles

Hazel N. Brenner·James S. Depret-Guillaume·Eyvindur A. Palsson·Steven Senger
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Abstract

In this paper, we show that the maximum number of points in $d\geq3$ dimensions determining exactly 2 distinct triangles is $2d$. We further show that this maximum is uniquely achieved by the vertices of the $d$-orthoplex. We build upon the work of Hirasaka and Shinohara who determined that the $d$-orthoplex is such an optimal configuration, but did not prove its uniqueness. Further, we present a more elementary argument for its optimality.

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Hazel N. Brenner, James S. Depret-Guillaume, Eyvindur A. Palsson, Steven Senger. 2019-10-01. Uniqueness of Optimal Point Sets Determining Two Distinct Triangles. https://doi.org/10.5281/zenodo.10816792

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