  Let $X$ be a simply connected CW complex with finite rational cohomology. For
the finite quotient set of rationalized orbit spaces of $X$ obtained by almost
free toral actions, ${\mathcal T}_0(X)=\{[Y_i] \}$, induced by an equivalence
relation based on rational toral ranks, we order as $[Y_i]<[Y_j]$ if there is a
rationalized Borel fibration $Y_i\to Y_j\to BT^n_{\Q}$ for some $n>0$. It
presents a variation of almost free toral actions on $X$. We consider about the
Hasse diagram ${\mathcal H}(X)$ of the poset ${\mathcal T}_0(X)$, which makes a
based graph $G{\mathcal H}(X)$, with some examples. Finally we will try to
regard $G{\mathcal H}(X)$ as the 1-skeleton of a finite CW complex ${\mathcal
T}(X)$ with base point $X_{\Q}$.
