  We investigate the generalization of the Costas property in 3 or more
dimensions, and we seek an appropriate definition; the 2 main complications are
a) that the number of ``dots'' this multidimensional structure should have is
not obvious, and b) that the notion of the multidimensional permutation needs
some clarification. After proposing various alternatives for the generalization
of the definition of the Costas property, based on the definitions of the
Costas property in 1 or 2 dimensions, we also offer some construction methods,
the main one of which is based on the idea of reshaping Costas arrays into
higher-dimensional entities.
