SummaryRecent papers considered the question of figurate numbers being polygonal, looking at triangular numbers and, more generally, perfect powers (triangles, squares, cubes). Here we continue these investigations in a slightly different direction, considering the question of simplex numbers (triangles, tetrahedra, pentatopes). We find, among other things, that asymptotically almost all simplex numbers are polygonal.
Ponomarenko et al. (Thu,) studied this question.