We derive and present systematic relationships between the analytical formulas for calculation of the localized surface plasmon resonances (LSPR) of some plasmonic nanostructures which we have categorized as simple. These relationships, including some new formulas, are summarized in a tree diagram which highlights the core-shell plasmons as the generators of solid and cavity plasmons. In addition, we show that the LSPR of complex structures can be reduced to that of simpler ones, using the LSPR of a nanorice as a case study, in the dipole limit. All the formulas were derived using a combination of the Drude model, the Rayleigh approximation, and the Fröhlich condition. The formulas are handy and they are in good agreement with the results of the plasmon hybridization theory. The formulas also account for dielectric effects, which provide versatility in the tuning of the LSPR of the nanostructures. A simplified model of plasmon hybridization is presented, allowing us to investigate the weak-coupling regimes of solid and cavity plasmons in the core-shell nanostructures we have studied.