Let $X=X_\Delta$ be the toric variety associated to a reflexive polyhedron $\Delta$. Consider a Calabi-Yau hypersurface $Y\subset X$, and the image of $Y$ under the moment map $\mu:X\to \Delta$ has the shape of an amoeba.
Let's focus on the special case when $Y$ is a K3 surface given by a quartic in $X=X_\Delta=\mathbb {CP}^3$. Recall that $\Delta$ is the integral 3-simplex with vertices $(-1,-1,-1), (-1,-1,3),(-1,3,-1),(3,-1,-1)$. What I know is that there are exactly four points in $\mu(Y)$ on every edge of $\Delta$.
But, I would like to ask for a good reference for the figure of the amoeba $\mu(Y)\subset \Delta$ for the K3 surface $Y$. Moreover, I would like to know how does the equation of the quartic determine the shape of the amoeba. Thanks!
