There are many structured P2P systems that use DHT technologies to map data items onto the nodes in various ways for scalable routing and location. Most of the systems require O(log n) hops per lookup request with O(log n) neighbors per node, where n is the network size. In this paper, we present a constant-degree P2P architecture, namely Cycloid, which emulates a CubeConnected-Cycles (CCC) graph in the routing of lookup requests. It achieves a time complexity of O(d) per lookup request by using O(1) neighbors per node, where n = d