In this paper, we propose OWCells, a class of optical wireless cellular data center network architectures in which fixed line of sight (LOS) optical wireless communication (OWC) links are used to connect racks of servers arranged in regular polygonal topologies. We present the OWCell DCN architecture, develop its theoretical underpinnings, and investigate routing protocol and OWC transceiver design. Simulations are conducted to validate and compare the performance of OWCell. The impact of OWCell design parameters on its performance is also investigated. We compare the performance of OWCell using OCS and hybrid (OCS+OBS) switching schemes. The performance of OWCell is comparatively evaluated with HyScale DCN, a switch-centric hybrid optical DCN. Simulation results show that OWCell can reduce the number of links up by 95-98% while maintaining a performance that is within 15-25% that of HyScale. We discuss future research directions and approaches to improve the performance of the proposed OWCell DCN architectures.