Consider the equigenerated monomial ideal $I \subseteq k[x_1, \ldots ,x_n]$ and the well known inequality formula $\mu (I^2) \geq \ell(I) \mu(I)- {{\ell(I)}\choose{2}}$, where $\mu(I)$ is the minimal number of generators of the monomial ideal $I$ and $\ell(I)$ is the dimension of fiber cone $F(I)$. This inequality is called Freiman inequality and in the case of equality Herzog and Zhu \cite{HZ} called the ideal a Freiman ideal. Furthermore, they raised a question about the classification of all Freiman Veronese type ideals. In this paper, we determine some cases of Veronese type ideals which are Freiman. Additionaly, we characterize polymatroidal Freiman ideals of degree two.
