  Multi-dimensional cyclic code is a natural generalization of cyclic code. In
an earlier paper we explored two-dimensional constacyclic codes over finite
fields. Following the same technique, here we characterize the algebraic
structure of multi-dimensional constacyclic codes, in particular
three-dimensional $(\alpha,\beta,\gamma)$- constacyclic codes of arbitrary
length $s\ell k$ and their duals over a finite field $\mathbb{F}_q$, where
$\alpha,\beta,\gamma$ are non zero elements of $\mathbb{F}_q$. We give
necessary and sufficient conditions for a three-dimensional
$(\alpha,\beta,\gamma)$- constacyclic code to be self-dual.
