We theoretically studied the optical properties of Ag nanoparticles (NPs) with different morphologies by measuring the electron energy loss spectra (EELS) of different localized surface plasmon (LSP) resonance modes with the boundary element method (BEM). And we use the group theory to explain qualitatively how LSP modes and the corresponding degeneracies evolve as the curvature changes by classifying them based on irreducible (IR) representations, and link it with the change of EELS and EELS maps. Besides, we construct a nanodimer with nano torus monomers and discuss some interesting coupling phenomena cause by the deviations of the principal axis in symmetry group compared with monomer cases. Then we show that LSP modes in both monomers and dimers are high refractive sensitive (RIS) when we change the dielectric around NPs.