Abstract: Among others we will prove that the equational theory of omega dimensional representable polyadic equality algebras is not schema axiomatizable. This result is in contrast with the Daigneault-Monk representation theorem which states that the class of representable polyadic algebras is finite schema-axiomatizable (and hence the equational theory of this class is finite schema-axiomatizable, too). We will also show that the complexity of the equational theory of the class of omega dimensional representable polyadic equality algebras is also extremely high in the recursion theoretic sense. Finally, comparing our negative results with the positive ones of Ildiko Sain and Viktor Gyuris, we will draw the following methodological conclusions. The negative properties of polyadic (equality) algebras can be removed by switching from the so called "polyadic algebraic paradigm" to the "cylindric algebraic" one.