Hexakis[4-(2,4-diamino-1,3,5-triazin-6-yl)phenyl]benzene (4) incorporates a disc-shaped hexaphenylbenzene core and six peripheral diaminotriazine groups that can engage in hydrogen bonding according to established motifs. Under all conditions examined, compound 4 crystallizes as planned to give closely related noninterpenetrated three-dimensional networks built from sheets in which each molecule has six hydrogen-bonded neighbors. In the structure of compound 4, the number of hydrogen bonds per molecule and the percentage of volume accessible to guests approach the highest values so far observed in molecular networks. Analogue 5 (which has the same hexaphenylbenzene core but only four diaminotriazine groups at the 1,2,4,5-positions) and analogue 7 (in which the two unsubstituted phenyl groups of compound 5 are replaced by methyl groups) crystallize according to a closely similar pattern. Analogues with flatter pentaphenylbenzene or tetraphenylbenzene cores crystallize differently, underscoring the importance of maintaining a consistent molecular shape in attempts to engineer crystals with predetermined properties.