This work analyzes and develops some fundamental results for attitude consensus control of a network of rigid-body vehicles, considered a multi-agent rigid body system (MARBS). The system is analyzed using a full rigid body dynamics model on TSO(3) for each vehicle (agent) in the network. Therefore, the state space of the system is TSO(3)N, where N is the number of vehicles. Attitude synchronization control laws for each vehicle to reach a consensus attitude with zero angular velocity for a particular type of network are obtained, using a Morse-Lyapunov function. Some fundamental results on equilibria of the network under these attitude consensus control laws are obtained. We show that unlike cooperative control of multi-agent systems with highly simplified dynamics models for agents, like point particles or unicycles where the state space of the dynamics is modeled as a vector space, there are multiple equilibrium solutions possible for attitude consensus control laws for a MARBS with dynamics on TSO(3)N. Further, the number of equilibria depends on the network graph topology. This is followed by numerical simulation results for two different network graphs, which show this network control framework to be effective in obtaining attitude consensus.