The zero-dimensional (0D) metal halides comprising isolated metal-halide polyhedra are the smallest inorganic quantum systems and accommodate quasi-localized Frenkel excitons with unique photophysics of broadband luminescence, huge Stokes shift, and long lifetime. Little is known about the role of polyhedron type in the characteristics of 0D metal halides. We comparatively study three novel kinds of 0D hybrid tin halides having identical organic groups. They are efficient light emitters with a maximal quantum yield of 92.3%. Their most stable phases are composed of octahedra for the bromide and iodide but disphenoids for the chloride. They separately exhibit biexponential and monoexponential luminescence decays due to different symmetries and electronic structures. The chloride has the largest absorption and smallest emission photon energies. A proposed model regarding unoccupied-energy-band degeneracy explains well the experimental phenomena and reveals the crucial role of polyhedron type in determining optical properties of the 0D tin halides.