Large regular simplices contained in a hypercube with a common barycenter

Details Large regular simplices contained in a hypercube with a common barycenter Large regular simplices contained in a hypercube with a common barycenter

2011-01-14

arxiv.org/abs/1101.2707v1

Mathematics

Metric Geometry

5 pages

Scientific paper

It has been shown that the $n$-dimensional unit hypercube contains an
$n$-dimensional regular simplex of edge length $c\sqrt n$ for arbitrary $c<1/2$
if $n$ is sufficiently large (Maehara, Ruzsa and Tokushige, 2009). We prove the
same statement holds for some $c>1/2$ even in the special case where a regular
simplex has the same barycenter as that of the unit hypercube.

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