Nanostructures of some metals can sustain light-driven electron oscillations called localized surface plasmon resonances, or LSPRs, that give rise to absorption, scattering, and local electric field enhancement. Their resonant frequency is dictated by the nanoparticle (NP) shape and size, fueling much research geared toward discovery and control of new structures. LSPR properties also depend on composition; traditional, rare, and expensive noble metals (Ag, Au) are increasingly eclipsed by earth-abundant alternatives, with Mg being an exciting candidate capable of sustaining resonances across the ultraviolet, visible, and near-infrared spectral ranges. Here, we report numerical predictions and experimental verifications of a set of shapes based on Mg NPs displaying various twinning patterns including (101̅1), (101̅2), (101̅3), and (112̅1), that create tent-, chair-, taco-, and kite-shaped NPs, respectively. These are strikingly different from what is obtained for typical plasmonic metals because Mg crystallizes in a hexagonal close packed structure, as opposed to the cubic Al, Cu, Ag, and Au. A numerical survey of the optical response of the various structures, as well as the effect of size and aspect ratio, reveals their rich array of resonances, which are supported by single-particle optical scattering experiments. Further, corresponding numerical and experimental studies of the near-field plasmon distribution via scanning transmission electron microscopy electron-energy loss spectroscopy unravels a mode nature and distribution that are unlike those of either hexagonal plates or cylindrical rods. These NPs, made from earth-abundant Mg, provide interesting ways to control light at the nanoscale across the ultraviolet, visible, and near-infrared spectral ranges.