The development of rigid covalent chiroptical organic materials, with multiple, readily available redox states, which exhibit high photoluminescence is of particular importance in relation to both organic electronics and photonics. The chemically stable, thermally robust and redox-active perylene diimide (PDI) fluorophores have received ever-increasing attention owing to their excellent fluorescence quantum yields in solution. Planar PDI derivatives, however, generally suffer from aggregation-caused emission quenching in the solid state. Herein, we report on the design and synthesis of two chiral isosceles triangles wherein one PDI fluorophore and two pyromellitic diimide (PMDI) or naphthalene diimide (NDI) units are arranged in a rigid cyclic triangular geometry. The optical, electronic and magnetic properties of the rigid isosceles triangles are fully characterized by a combination of optical spectroscopies, X-ray diffraction, cyclic voltammetry, and computational modeling techniques. Single-crystal X-ray diffraction analysis shows that both isosceles triangles form discrete, nearly cofacial PDI-PDI π-dimers in the solid state. While the triangles exhibit fluorescence quantum yields of almost unity in solution, the dimers in the solid state exhibit very weak-yet at least an order of magnitude higher-excimer fluorescence yield in comparison with the almost completely quenched fluorescence of a reference PDI. The triangle containing both NDI and PDI subunits shows superior intramolecular energy transfer from the lowest excited singlet state of the NDI to that of the PDI subunit. Cyclic voltammetry suggests that both isosceles triangles exhibit multiple, easily accessible and reversible redox states. Applications beckon in arenas related to molecular optoelectronic devices.