  A dynamic procedure is established within the generalised Tavis-Cummings
model to generate light states with discrete point symmetries, given by the
cyclic group ${\cal C}_n$. We consider arbitrary dipolar coupling strengths of
the atoms with a one-mode electromagnetic field in a cavity. The method uses
mainly the matter-field entanglement properties of the system, which can be
extended to any number of $3$-level atoms. An initial state constituted by the
superposition of two states with definite total excitation numbers, $\vert \psi
\rangle_{M_1}$, and $\vert \psi \rangle_{M_2}$, is considered. It can be
generated by the proper selection of the time-of-flight of an atom passing
through the cavity. We demonstrate that the resulting Husimi function of the
light is invariant under cyclic point transformations of order $n=\vert
M_1-M_2\vert$.
