  Let $G_n$ be a non-extensible, flexible closed curve of length $n$ in the
3-space $\R^3$ with $n$ particles $A_1$,...,$A_n$ evenly fixed (according to
the arc length of $G_n$) on the curve. Let $f:(0, \infty)\to \R$ be an
increasing and continuous function. Define an energy function
  $$E^f_n(G_n)= \sum_{p< q} f(|A_pA_q|),$$ where $|A_pA_q|$ is the distance
between $A_p$ and $A_q$ in $\R^3$. We address a natural and interesting
problem: {\it What is the shape of $G_n$ when $E^f_n(G_n)$ reaches the maximum?
}
  In many natural cases, one such case being $f(t) = t^\alpha$ with $0 < \alpha
\le 2$, the maximizers are regular $n$-gons and in all cases the maximizers are
(possibly degenerate) convex $n$-gons with each edge of length 1.
