The valency (connectivity) of building units in covalent organic frameworks (COFs) has been primarily 3 and 4, corresponding to triangles and squares or tetrahedrons, respectively. We report a strategy for making COFs with valency 8 (cubes) and "infinity" (rods). The linker 1,4-boronophenylphosphonic acid-designed to have boron and phosphorus as an isoelectronic combination of carbon-group elements-was condensed into a porous, polycubane structure (BP-COF-1) formulated as (-B4P4O12-)(-C6H4-)4. It was characterized by x-ray powder diffraction techniques, which revealed cubes linked with phenyls. The isoreticular forms (BP-COF-2 to 5) were similarly prepared and characterized. Large single crystals of a constitutionally isomeric COF (BP-COF-6), composed of rod units, were also synthesized using the same strategy, thus propelling COF chemistry into a new valency regime.