  A rule for constructing interpolation nodes for $n$th degree polynomials on
the simplex is presented. These nodes are simple to define recursively from
families of 1D node sets, such as the Lobatto-Gauss-Legendre (LGL) nodes. The
resulting nodes have attractive properties: they are fully symmetric, they
match the 1D family used in construction on the edges of the simplex, and the
nodes constructed for the $(d-1)$-simplex are the boundary traces of the nodes
constructed for the $d$-simplex. When compared using the Lebesgue constant to
other explicit rules for defining interpolation nodes, the nodes recursively
constructed from LGL nodes are nearly as good as the "warp & blend" nodes of
Warburton in 2D (which, though defined differently, are very similar), and in
3D are better than other known explicit rules by increasing margins for $n >
6$. By that same measure, these recursively defined nodes are not as good as
implicitly defined nodes found by optimizing the Lebesgue constant or related
functions, but such optimal node sets have yet to be computed for the
tetrahedron. A reference python implementation has been distributed as the
`recursivenodes` package, but the simplicity of the recursive construction
makes them easy to implement.
