  We present a thorough investigation of the electromagnetic resonant modes
supported by systems of polaritonic rods placed at the vertices of canonical
polygons. The study is conducted with rigorous finite-element eigenvalue
simulations. To provide physical insight, the simulations are complemented with
coupled mode theory (the analog of LCAO in molecular and solid state physics)
and a lumped wire model capturing the coupling-caused reorganizations of the
currents in each rod. The systems of rods, which form all-dielectric cyclic
metamolecules, are found to support the unconventional toroidal dipole mode,
consisting of the magnetic dipole mode in each rod. Besides the toroidal modes,
the spectrally adjacent collective modes are identified. The evolution of all
resonant frequencies with rod separation is examined. They are found to
oscillate about the single-rod magnetic dipole resonance, a feature attributed
to the leaky nature of the constituent modes. Importantly, we observe that
ensembles of an odd number of rods produce larger frequency separation between
the toroidal mode and its neighbor than the ones with even number of rods. This
increased spectral isolation, along with the low quality factor exhibited by
the toroidal mode, favors the coupling of the commonly silent toroidal dipole
to the outside world, rendering the proposed structure a prime candidate for
controlling the observation of toroidal excitations and their interaction with
the usually present electric dipole
