3D Cox-Little-Oshea

f(x,y,z)= A x^2 + B y^2 z^2 + C z^3

The level set of this function with A=1, B= -1, C=1 adorns the front cover of Ideals, Varieties, and Algorithms by D. Cox, J. Little, and D. O'Shea, Springer, 1992. The level set contains an entire curve of singularities.