  For generic $r=(r_1,\ldots,r_n) \in \mathbb{R}^n_+$ the space
$\mathcal{M}(r)$ of $n$--gons in $\mathbb{R}^3$ with edges of lengths $r$ is a
smooth, symplectic manifold. We investigate its Gromov width and prove that the
expression $$2\pi \min \{2 r_j, (\sum_{i \neq j} r_i) - r_j\,\,|\,
j=1,\ldots,n\}$$ is the Gromov width of all (smooth) $5$--gon spaces and of
$6$--gon spaces, under some condition on $r \in \mathbb{R}^6_+$. The same
formula constitutes a lower bound for all (smooth) spaces of $6$--gons.
Moreover, we prove that the Gromov width of $\mathcal{M}(r)$ is given by the
above expression when $\mathcal{M}(r)$ is symplectomorphic to
$\mathbb{C}\mathbb{P}^{n-3}$, for any $n \geq 4$.
