\ytableaushort{111}\quad 
\ytableaushort{222}\quad 
\ytableaushort{333}\quad
\ytableaushort{112}\quad
\ytableaushort{113}\quad
\ytableaushort{122}\quad
\ytableaushort{133}\quad
\ytableaushort{223}\quad
\ytableaushort{233}\quad
\ytableaushort{123}$$ and the associated Schur polynomial is $$s_{(3,0,0)}(\x) = 
x_1^3+x_2^3+x_3^3
+ x_1^2x_2+x_1^2x_3+x_1x_2^2+x_1x_3^2+x_2^2x_3+x_2x_3^2  
+x_1x_2x_3.$$ The Newton polytope ${\mathrm{Newt}}(s_{(3,0,0)}(\x))$ is the convex hull of the points $$(3,0,0),(2,1,0),(2,0,1),(1,2,0),(1,1,1),(1,0,2),(0,3,0),(0,2,1),(0,1,2),(0,0,3)
.$$

\[ex:(2,1)\] Consider the partition $\lambda=(2,1,0)\vdash 3$. Let $m=3$ and $\x = (x_1,x_2,x_3)$. The semistandard Young tableaux are $$\ytableaushort{11,2}\quad
\ytableaushort{11,3}\quad
\ytableaushort{12,2}\quad
\ytableaushort{13,3}\quad
\ytableaushort{22,3}\quad
\ytableaushort{23,3}\quad
\ytableaushort{12,3}\quad
\ytableaushort{13,2}$$ and the associated Schur polynomial is $$s_{(2,1,0)}(\x) = 
x_1^2x_2+x_1^2x_3+x_1x_2^2+x_1x_3^2+x_2^2x_3+x_2x_3^2+2x_1x_2x_3.$$ The Newton polytope ${\mathrm{Newt}}(s_{(2,1,0)}(\x))$ is the convex hull of the points $$(2,1,0),(2,0,1),(1,2,0),(1,0,2),(0,2,1),(0,1,2),(1,1,1).$$

Since Schur polynomials are homogeneous polynomials, we have that ${\mathrm{Newt}}(s_\lambda(x_1,\ldots, x_m))$ is an $(m-1)$-dimensional polytope in $\mathbb{R}^m$. Consequently, the polytopes for the Schur polynomials in Example \[ex:(3)\] and Example \[ex:(2,1)\] are $2$-dimensional polytopes in $\mathbb{R}^3$. In Figure \[fig:schur\], we have depicted these polytopes (equivalently) in the plane for convenience. It is known that Schur polynomials have SNP [@Monical-Tokcan-Yong Proposition 2.5].

![Newton polytopes for Schur polynomials in Example \[ex:(3)\] (left) and Example \[ex:(2,1)\] (right) drawn in $\mathbb{R}^2$ rather than in a $2$-dimensional subspace of $\mathbb{R}^3$. Both of these polytopes can be shown to be reflexive if we translate them so that their unique interior point is $(0,0)$.[]{data-label="fig:schur"}](SageImage-schur_3_3-reflexive-triangle.png "fig:"){height="3.5cm"} ![Newton polytopes for Schur polynomials in Example \[ex:(3)\] (left) and Example \[ex:(2,1)\] 