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Hurewicz theorem says that for a simply connected space $X$, $\pi_2(X)\cong H_2(X,\mathbb Z)$. So $\pi_2(K3)\cong H_2(K3,\mathbb Z)\cong \mathbb Z^{20}$Z^{22}$. Here is a link:

http://en.wikipedia.org/wiki/Hurewicz_theorem

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Hurewicz theorem says that for a simply connected space $X$, $\pi_2(X)\cong H_2(X,\mathbb Z)$. So $\pi_2(K3)\cong \mathbb Z^{20}$. Here is a link:

http://en.wikipedia.org/wiki/Hurewicz_theorem