  We study $3$-folds with an action of a algebraic torus $T$ and finite fixed
point set. In particular, assuming the torus action has (exactly) $6$ fixed
points we show that aside from Mori fibre spaces, the topology of such spaces
is strongly restricted. For $T= \mathbb{C}^{*}$ we prove that there are two
explicit infinite families plus a finite number of exceptional cases. For $T =
\mathbb{C}^{*} \times \mathbb{C}^{*}$ there are $2$ exceptional cases which are
described explicitly.
