Extreme and exposed points of spaces of integral polynomials

We show that if $E$ is a real Banach space such that $E'$ has the approximation property and such that $\ell_1\not\hookrightarrow {\widehat \bigotimes_{n,s,\epsilon}} E$, then the set of extreme points of the unit ball of $\mathcal{P}_I(^nE)$ is equal to $\{\pm\phi^n\colon \phi\in E',\Vert\phi\Vert=1\}$. Under the additional assumption that $E'$ has a countable norming set, we see that the set of exposed points of the unit ball of $\mathcal{P}_I(^nE)$ is also equal to $\{\pm\phi^n\colon \phi\in E',\Vert\phi\Vert=1\}$.