  Let $P=A_1\ldots A_n$ be a generic polygon in three-dimensional space and let
$v_1,v_2,\ldots,v_n$ be vectors
$\overline{A_1A_2},\overline{A_2A_3},\ldots,\overline{A_nA_1}$, respectively.
$P$ will be called \emph{regular}, if there exist vectors $u_1,\ldots,u_n$ such
that cross products $[u_1,u_2],[u_2,u_3],\ldots,[u_n,u_1]$ are equal to vectors
$v_2,v_3,\ldots,v_1$, respectively. In this case the polygon $P'$, defined be
vectors $u_2-u_1,u_3-u_2,\ldots,u_1-u_n$ will be called the \emph{derived
polygon} or the \emph{derivative} of the polygon $P$. In this work we formulate
conditions for regularity and discuss geometric properties of derived polygons
for $n=4,5,6$.
