= Solution
The interior values satisfy $-1/27<f<0$ away from the <minimum>. The <contours> are closed curves surrounding $(1/3,-1/3)$, approximately <ellipses> near that point, and approach the three edges as the level tends to zero. To see their shape globally, put $u=x$, $v=-y$, $w=1-x+y$. These are positive inside and satisfy $u+v+w=1$, while $f=-uvw$. Since $\log(uvw)=\log u+\log v+\log w$ is strictly <concave>, its nonempty superlevel sets are convex and surround the unique maximum of $uvw$. Thus the negative contours nest without additional components, as in the figure.
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