  In the following text we compute possible heights of $\mathbb A$ (Alexandroff
square), $\mathbb O$ (unit square $[0,1]\times[0,1]$ with lexicographic order
topology) and $\mathbb U$ (unit square $[0,1]\times[0,1]$ with induced topology
of Euclidean plane). We prove $P_h(\mathbb{A})=\{n:n\geq5\}\cup\{+\infty\}$,
$P_h(\mathbb{O})=\{n:n\geq4\}\cup\{+\infty\}$,
$P_h(\mathbb{U})=\{n:n\geq1\}\cup\{+\infty\}$ (where for topological space $X$,
by $P_h(X)$ we mean the collection of heights of transformation groups with
phase space $X$. In this way we also prove that there is not any topological
transitive (resp. Devaney chaotic) Alexandroff square transformation group.
