For generic r = (r1, … , rn) ∈ $$ {\mathrm{\mathbb{R}}}_{+}^n $$ the space ℳ(r) of n–gons in ℝ3 with edges of lengths r is a smooth, symplectic manifold. We investigate its Gromov width and prove that the expression 2π min {2r j , (∑ i ≠ j r i ) − r i |j = 1, … , n} is the Gromov width of all (smooth) 5–gon spaces and of 6–gon spaces, under some condition on r ∈ $$ {\mathrm{\mathbb{R}}}_{+}^6 $$ . The same formula constitutes a lower bound for all (smooth) spaces of 6–gons. Moreover, we prove that the Gromov width of ℳ(r) is given by the above expression when ℳ(r) is symplectomorphic to ℂℙ n − 3, for any n ≥ 4.