The present study deals with the structural characterization and classification of the novel compounds 1-8 into perovskite subclasses and proceeds in extracting the structure-band gap relationships between them. The compounds were obtained from the employment of small, 3-5-atom-wide organic ammonium ions seeking to discover new perovskite-like compounds. The compounds reported here adopt unique or rare structure types akin to the prototype structure perovskite. When trimethylammonium (TMA) was employed, we obtained TMASnI(3) (1), which is our reference compound for a "perovskitoid" structure of face-sharing octahedra. The compounds EASnI(3) (2b), GASnI(3) (3a), ACASnI(3) (4), and IMSnI3 (5) obtained from the use of ethylammonium (EA), guanidinium (GA), acetamidinium (ACA), and imidazolium (IM) cations, respectively, represent the first entries of the so-called "hexagonal perovskite polytypes" in the hybrid halide perovskite library. The hexagonal perovskites define a new family of hybrid halide perovskites with a crystal structure that emerges from a blend of comer- and face-sharing octahedral connections in various proportions. The small organic cations can also stabilize a second structural type characterized by a crystal lattice with reduced dimensionality. These compounds include the two-dimensional (2D) perovskites GA(2)SnI(4) (3b) and IPA(3)Sn(2)I(7) (6b) and the one-dimensional (1D) perovskite IPA(3)SnI(5) (6a). The known 2D perovskite BA(2)MASn(2)I(7) (7) and the related all-inorganic 1D perovskite "RbSnF2I" (8) have also been synthesized. All compounds have been identified as medium-to-wide-band-gap semiconductors in the range of E-g = 1.90-2.40 eV, with the band gap progressively decreasing with increased corner-sharing functionality and increased torsion angle in the octahedral connectivity.