Standard terminology for the operator $(a,b,c,d) \mapsto (b*c*d, a*c*d, a*b*d, a*b*c)$

Question

Is there a standard name for the operator $s(a,b,c,d) := (bcd, acd, abd, abc)$ ? More generally, $s(x_1,x_2,...,x_n) = (z_1,\ldots,z_n)$, where $z_i = \prod_{j \ne i} x_j$.