The notion of a core is generalized to multiway networks. To determine the multiway cores, we adapted already-known algorithms for determining the generalized cores in one-mode and two-mode networks. A new node property, node diversity has been introduced. The newly introduced notions are illustrated with application on the multiway networks of European airports and airlines and Summer Olympic medals till 2016. For the interactive inspection of the results, their 3D layout in X3D is supported.