  For an action of a compact torus $T$ on a smooth compact manifold~$X$ with
isolated fixed points the number $\frac{1}{2}\dim X-\dim T$ is called the
complexity of the action. In this paper we study certain examples of torus
actions of complexity one and describe their orbit spaces. We prove that
$\mathbb{H}P^2/T^3\cong S^5$ and $S^6/T^2\cong S^4$, for the homogeneous spaces
$\mathbb{H}P^2=Sp(3)/(Sp(2)\times Sp(1))$ and $S^6=G_2/SU(3)$. Here the maximal
tori of the corresponding Lie groups $Sp(3)$ and $G_2$ act on the homogeneous
spaces by the left multiplication. Next we consider the quaternionic analogues
of smooth toric surfaces: they give a class of 8-dimensional manifolds with the
action of $T^3$, generalizing $\mathbb{H}P^2$. We prove that their orbit spaces
are homeomorphic to $S^5$ as well. We link this result to Kuiper--Massey
theorem and some of its generalizations.
