A figurate number corresponding to a configuration of points which form a pyramid with -sided regular polygon bases
can be thought of as a generalized pyramidal number, and has the form

Conway, J. H. and Guy, R. K. "Tetrahedral Numbers" and "Square Pyramidal Numbers" The
Book of Numbers. New York: Springer-Verlag, pp. 44-49, 1996.Sloane,
N. J. A. and Plouffe, S. "Pyramidal Numbers." Extended entry
for sequence M3382 in The
Encyclopedia of Integer Sequences. San Diego, CA: Academic Press, 1995.