Covalent organic frameworks (COFs) are an emerging class of highly ordered porous polymers with many potential applications. They are currently designed and synthesized through hexagonal and tetragonal topologies, limiting the access to and exploration of new structures and properties. Here, we report that a triangular topology can be developed for the rational design and synthesis of a new class of COFs. The triangular topology features small pore sizes down to 12 Å, which is among the smallest pores for COFs reported to date, and high π-column densities of up to 0.25 nm⁻², which exceeds those of supramolecular columnar π-arrays and other COF materials. These crystalline COFs facilitate π-cloud delocalization and are highly conductive, with a hole mobility that is among the highest reported for COFs and polygraphitic ensembles.