Abstract: A parallel processing computer having a three dimensional (3D) torus topology. The computer includes multiple nodes formed in rows, multiple leap frog connections, and multiple end connections. The rows extend into the X, Y, and Z dimensions. The 3D torus topology of the present invention is achieved as follows. Along every row, end nodes are connected to adjacent nodes by the end connections. Also, along every row, alternate nodes are connected by the leap frog connections. Thus, the use of the leap frog connections results in an alternating connection pattern among the nodes.