  In this work, a family of symmetric interpolation points are generated on the
four-dimensional simplex (i.e. the pentatope). These points are optimized in
order to minimize the Lebesgue constant. The process of generating these points
closely follows that outlined by Warburton in "An explicit construction of
interpolation nodes on the simplex," Journal of Engineering Mathematics, 2006.
Here, Warburton generated optimal interpolation points on the triangle and
tetrahedron by formulating explicit geometric warping and blending functions,
and applying these functions to equidistant nodal distributions. The locations
of the resulting points were Lebesgue-optimized. In our work, we extend this
procedure to four dimensions, and construct interpolation points on the
pentatope up to order ten. The Lebesgue constants of our nodal sets are
calculated, and are shown to outperform those of equidistant nodal
distributions.
