We have calculated the electronic properties and layer stacking patterns for a group of twelve hexagonal covalent organic frameworks. This has been done in order to explore this group of materials on a fundamental level and aim to lay the ground work for further studies, which will focus on assessing these frameworks as useful materials for electronic and optoelectronic devices. To explore these materials, we have deployed numerical density functional theory calculations. A Van der Waals density functional is used to describe non-local correlation effects that give rise to stabilizing van der Waals forces, essential in layered systems. We found that all the materials prefer to stack in specific configurations close to AA-stacking, where subsequent layers are placed directly on-top of each other. We also found that the materials exhibit dispersion in the out-of-plane direction when we go from two-dimensional single layers to three-dimensional stacks.