Recursive Diagonal Torus (RDT), a class of interconnection network is proposed for massively parallel computers with up to 216 nodes. By adding remote links to the diagonal directions of the torus network recursively, the RDT can realize a smaller diameter (eg., it is 11 for 216 nodes) with small number of links per node (i.e., 8 links per node) than that of the hypercube. A simple routing algorithm called vector routing, which is near-optimal and easy to implement is also proposed. The RDT comprises the mesh structure, and emulates hypercube and tree structures easily. FFT and the bitonic sorting algorithm are also easy to implement.