# On the Width of the Regular n-Simplex

arXiv: https://arxiv.org/abs/2301.02616 · HTML: https://mlsanity.com/paper/2301.02616/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jan 2023.

## Built on by (most cited first, 1 of 1)

- [Towards the mathematical foundation of the minimum enclosing ball and related problems](https://mlsanity.com/paper/2402.06629/) (2024)

## Abstract (arXiv)

Consider the regular n-simplex Deltan - it is formed by the convex-hull of n+1 points in Euclidean space, with each pair of points being in distance exactly one from each other. We prove an exact bound on the width of Deltan which is ≈ √2/n. Specifically,  width(Deltan) = √frac2n + 1 if n is odd, and  width(Deltan) = √frac2(n+1)n(n+2)  if n is even. While this bound is well known [GK92, Ale77], we provide a self-contained elementary proof that might (or might not) be of interest.