Minkowski Sum And Mixed Faces

Let $P_1$ be the unit cube $[0,1]\times[0,1] \times[0,1]$ and $P_2$ be the standard simplex $\mathrm{conv}(0,e_1,e_2,e_3)$. Let $f_1,f_2$ be polynomials with Newton polytopes $P_1$ and $P_2$ respectively, with generic coefficients. Draw the Minkowski sum $P_1+P_2$ and identify the rays of $\mathcal{T}(\langle f_1,f_2\rangle)$ as normal to the "mixed faces" (try to give a definition of this.


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