As is well known, the geometry of the interpolation site of a multivariate
polynomial interpolation problem constitutes a dominant factor for the
structures of the interpolation polynomials. Solving interpolation problems on
interpolation sites with special geometries in theory may be a key step to the
development of general multivariate interpolation theory. In this paper, we
introduce a new type of 2-dimensional interpolation sites, tower interpolation
sites, whose associated degree reducing Lagrange interpolation monomial and
Newton bases w.r.t.