The projections in the $xy$-plane of these choreography has winding
number $l$ around a center and is invariant by rotations of
$2\pi/m$; and the bodies make groups of $h$ polygons, where $h$ is
maximum common divisor of $n$ and $k$.
The spatial choreographies along the vertical Lyapunov families are
symmetric by the two reflections $-y$ and $-z$, while the spatial
choreographies along the axial family are symmetric only by the
reflections $(-y,-z)$, when the $x$-axis is chosen to pass through
the \textquotedblleft center\textquotedblright of the orbit.
Each choreography is winding $l$ times around a center and invariant
by rotations of $2\pi/m$. Also, the bodies move in groups of $h$
polygons, where $h$ is maximum common divisor of $n$ and $k$. In
addition, these choreographies are symmetric by a reflection in the
plane.
