Improved Lebesgue constants on the triangle

New sets of points with improved Lebesgue constants in the triangle are calculated. Starting with the Fekete points a direct minimization process for the Lebesgue constant leads to better results. The points and corresponding quadrature weigths are explicitly given. It is quite surprising that the optimal points are not symmetric. The points along the boundary of the triangle are the 1D Gauss–Lobatto points. For all degrees, our points yield the smallest Lebesgue constants currently known. Numerical examples are presented, which show the improved interpolation properties of our nodes.