Lattices on simplicial partitions which are not simply connected (Q711238)

The existence and uniqueness of a \(d\)-variate Lagrange polynomial interpolant depends on the geometry of the interpolation points. In the case of a \((d+1)\)-pencil lattice [see \textit{S.~L.~Lee} and \textit{G.~M.~Phillips}, Constructive Approximation 7, No.~3, 283--297 (Zbl 0733.41011)], the interpolation points are generated as intersections of particular hyperplanes. In this paper, the author studies the case of \((d+1)\)-pencil lattices on simplicial partitions in \({\mathbb R}^d\), which are not simply connected.