  While every polyadic algebra ($\PA$) of dimension 2 is representable, we show
that not every atomic polyadic algebra of dimension two is completely
representable; though the class is elementary. Using higly involved
constructions of Hirsch and Hodkinson we show that it is not elementary for
higher dimensions a result that, to the best of our knowledge, though easily
destilled from the literature, was never published. We give a uniform flexible
way of constructing weak atom structures that are not strong, and we discuss
the possibility of extending such result to infinite dimensions. Finally we
show that for any finite $n>1$, there are two $n$ dimensional polyadic atom
structures $\At_1$ and $\At_2$ that are $L_{\infty,\omega}$ equivalent, and
there exist atomic $\A,\B\in \PA_n$, such that $\At\A=\At_1$ and $\At\B=
\At_2$, $\A\in \Nr_n\PA_{\omega}$ and $\B\notin \Nr_n\PA_{n+1}$. This can also
be done for infinite dimensions (but we omit the proof)
