In recent years, the enhancement of microchip technologies has enabled large scale Systems-on-Chip (SoC). Due to sharp increase in number of processing elements, SoC faces various challenges in design and testing. Network on Chip (NoC) is an alternative technology to overcome the challenges in SoC design and testing. NoC emerged as a key architecture that allows one to optimize the parameters like power andarea. Inspiteofitsapplications, NoCfacessomerealtimechallengeslikedesigning an optimum topology, routing scheme and application mappings. In this paper, we address the main three issues on NoC, namely, designing of an optimal topology, routing algorithm and a router design for the topology. First, we propose a topology and a routing algorithm. We prove that our recursive network topology is Hamiltonian connected and we propose an algorithm for data packet transmissions, which is free from cyclic deadlocks and the algorithm maximizes the congestion factor. Our experimental results show that the proposed topology gives better performance in terms of average latency and power than the other topologies. Finally, we propose a router architecture for our 3D-NoC. The router architecture is based on shared buffers. Also, our experimental results indicate that the proposed router architecture consumes less area and power than the Virtual Channel architecture.