Let
ℓ
¯
=
(
ℓ
1
,
…
,
ℓ
n
)
\overline {\ell }=(\ell _1,\ldots ,\ell _n)
be an
n
n
-tuple of positive real numbers, and let
N
(
ℓ
¯
)
N(\overline {\ell })
denote the space of equivalence classes of oriented
n
n
-gons in
R
3
\mathbb {R}^3
with consecutive sides of lengths
ℓ
1
,
…
,
ℓ
n
\ell _1,\ldots ,\ell _n
, identified under translation and rotation of
R
3
\mathbb {R}^3
. Using known results about the integral cohomology ring, we prove that its topological complexity satisfies
TC
(
N
(
ℓ
¯
)
)
=
2
n
−
5
\operatorname {TC}(N(\overline {\ell }))= 2n-5
, provided that
N
(
ℓ
¯
)
N(\overline {\ell })
is nonempty and contains no straight-line polygons.