Is there an equivalent formulation to the Fernandez - Guasti squircle equation for n-gons

Question

Is there an equivalent formulation to the Fernandez - Guasti squircle equation

(x\^2\*z\^2 + y\^2\*z\^2 - s\^2 c\^2 x\^2 y\^2 - (z\^4/c\^2) == 0 , defined over x,y in R) for triangles, pentagon and n-gons?

Thanks