  Existence and spatio-temporal symmetric patterns of periodic solutions to
second order reversible equivariant non-autonomous periodic systems with
multiple delays are studied under the Hartman-Nagumo growth conditions. The
method is based on using the Brouwer $D_1 \times \mathbb Z_2\times
\Gamma$-equivariant degree theory, where $D_1$ is related to the reversing
symmetry, $\mathbb Z_2$ is related to the oddness of the right-hand-side and
$\Gamma$ reflects the symmetric character of the coupling in the corresponding
network. Abstract results are supported by a concrete example with $\Gamma =
D_n$ -- the dihedral group of order $2n$.
