  In this paper we work with power algebras associated to hyperplane
arrangements. There are three main types of these algebras, namely, external,
central, and internal zonotopal algebras. We classify all external algebras up
to isomorphism in terms of zonotopes. Also, we prove that unimodular external
zonotopal algebras are in one to one correspondence with regular matroids. For
the case of central algebras we formulate a conjecture.
