Let $M$ be a matroid on a finite ground set $E$ with rank function $r$, and let $P_B(M)$ be its base polytope. For $x\in \mathbb R^E$ and $A\subset E$, write $x(A)=\sum_{e\in A}x_e$. Then
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\begin{align*}
P_B(M)=\{x\in\mathbb R^E : x_e\ge 0\text{ for all }e\in E,\ x(A)\le r(A)\text{ for all }A\subset E,\ x(E)=r(E)\}.
\end{align*}