Geodesic
On a Property of $n$-Dimensional Simplices
Matematičeskie zametki, Tome 87 (2010) no. 4, pp. 580-593

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Suppose that $n\in\mathbb N$ and $S$ is a simplex in $\mathbb R^n$, containing the cube $[0,1]^n$. It is proved that, for some $i=1,\dots,n$, the simplex $S$ contains an interval of length $n$ parallel to the $i$th coordinate axis. The relationship with questions arising in linear interpolation of continuous functions of $n$ variables is noted.
Keywords: $n$-dimensional simplex, polytope, barycentric coordinates, axial diameter, interpolation projection operator, Steiner symmetrization, Hadamard number. 
@article{MZM_2010_87_4_a9,
     author = {M. V. Nevskij},
     title = {On a {Property} of $n${-Dimensional} {Simplices}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {580--593},
     publisher = {mathdoc},
     volume = {87},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_87_4_a9/}
}
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M. V. Nevskij. On a Property of $n$-Dimensional Simplices. Matematičeskie zametki, Tome 87 (2010) no. 4, pp. 580-593. http://geodesic.mathdoc.fr/item/MZM_2010_87_4_a9/