Methods and apparatus to determine and implement multidimensional network topologies are disclosed. An example method disclosed herein comprises receiving an input parameter for determining a multidimensional network topology for a network interconnecting a plurality of devices, and determining a set of multidimensional network topologies, each multidimensional network topology of the set comprising a respective plurality of nodes to interconnect the plurality of devices, each node in each multidimensional network topology of the set being fully connected with all neighbor nodes in each dimension of the multidimensional network topology, and each multidimensional network topology of the set satisfying a first constraint based on the input parameter.