Can $n^d + 1$ unit right $d$-simplices cover a right $d$-simplex with shortest side $n + \epsilon$?

TL;DR

This paper generalizes Conway and Soifer's result, showing how a specific number of unit right d-simplices can cover a larger right d-simplex with a slightly longer side in higher dimensions.

Contribution

It extends a known 2D covering result to arbitrary dimensions, providing a new geometric covering bound for right d-simplices.

Findings

$n^d + 1$ unit right $d$-simplices suffice to cover a right $d$-simplex with side $n + psilon$

The result generalizes the 2D case of covering equilateral triangles

Provides bounds for covering higher-dimensional simplices

Abstract

In a famous short paper, Conway and Soifer show that $n^2 + 2$ equilateral triangles with edge length 1 can cover one with side $n + \epsilon$. We provide a generalization to $d$ dimensions.