Hexagonal hexaminophenyl benzene, tetragonal tetrakis(4-aminophenyl) ethane, and trigonal 1,3,5-tris(p-formylphenyl)benzene were all joined together by imine linkages to yield a 2D porous covalent organic framework with unprecedented tth topology, termed COF-346. Unlike the 5 simple existing 2D topologies reported in COFs, COF-346 has 3 kinds of vertices and 2 kinds of edges and is constructed with linkers of 3 kinds of connectivity, and thus represents a higher degree of complexity in COF structures. The success in crystallizing COF-346 was based on precisely chosen geometry and metrics of the linkers and error correction offered by dynamic imine formation. We also report two additional related COFs: a crystalline, porous COF, termed COF-360 with a rare kgd topology, as well as the first crystalline, porous COF with defected tth topology, termed COF-340.