On one extremal property of a regular simplex
  In this paper, we show that the $L_p$-error of asymmetric linear approximation of the quadratic function $Q({\mathbf x})=\sum_{j=1}^{d}x_j^2$ on simplices in $\RR^d$ of fixed volume is minimized on regular simplices. 
Vladislav Babenko, Yuliya Babenko, Nataliya Parfinovych, and Dmytro   Skorokhodov
math.NA math.SG