6 spheres with the + and - regions of Lamé products
6 spheres with the + and - regions of Lam
G. Lamé solved Laplace's equation $\Delta\phi=0$ by separation of variables in elliptic coordinates; this led him to study transcendental functions called Lamé functions, and defined by a second-order ordinary differential equation. Three solutions are shown here, by drawing on the Riemann sphere the sign of the real part of the function.
Showcase of this model is Case number 15
Courant-Hilbert. Methoden der Mathematischen Physik, Bd. I, 5. Chap. §9.