In this paper we present an optical hypercube local area network which employs both free-space optics as well as optical fiber interconnections. Each node of the hypercube consists of an optical routing switch (ORS) to which users connect through an optical interface unit (OIU), providing a hierarchical structure. Self electrooptic effect devices (SEEDs) and two-dimensional spatial light modulators (SLMs) are used to perform high speed packet switching in the optical domain, providing an all-optical path between source and destination nodes. Electrooptic conversions occur only at the source and destination, eliminating the electronic bottleneck at the intermediate nodes. The network requires no wavelength division multiplexing and can be implemented using currently available optical technology to achieve high-speed switching and routing with low power requirements.