Chebyshev nodes on compact intervals, say $[-1,1]$, are a well-known solution for minimizing the effect of Runge's phenomenon when using Lagrange's polynomial interpolation, see, e.g., here : https://en.wikipedia.org/wiki/Chebyshev_nodes

If we define the $d$-dimensional simplex by $\mathcal{S}_d = \{\mathbf{x}\in [0,1]^d : \sum_{i=1}^d x_i \leq 1\}$, what would be the appropriate Chebyshev nodes on the space $\mathcal{S}_d$ ?