Consider three different functions, $F_1(x,y,z)$, $F_2(x,y,z)$ and $F_3(x,y,z)$, in a 3D Euclidean space with Cartesian coordinates x, y and z. Setting $F_1$ to some value, say $v_1$, defines an isosurface of $F_1$ in this space. Similarly, let $v_2$ and $v_3$ define isosurfaces of $F_2$ and $F_3$.
Suppose these isosurfaces intersect each other. Let $L_{12}$ denote the locus of points on the intersection between the $F_1$ and $F_2$ isosurfaces. Similarly define $L_{23}$ and $L_{31}$.
Suppose it is the case that for certain values of $v_1$, $v_2$ and $v_3$ the following condition is satisfied: $$L_{12}=L_{23}=L_{31}$$
I want to learn more about such intersections (in particular, how one tests for the existence of such intersections) but I don't know how to begin my search because I don't know what they are called. Any help with the lingo or hyperlinks to good explanations much appreciated.