  We find the height of the third fission barrier $B_{III}$ and energy of the
third minimum $E_{III}$ in $^{232}$Th using the macroscopic - microscopic
model, very well tested in this region of nuclei. For the first time it is done
on an 8-dimensional deformation hypercube. The dipole distortion is included
among the shape variables to assure that no important shapes are missed. The
saddle point is found on a lattice containing more than 50 million points by
the immersion water flow (IWF) method. The shallow third minimum,
$B_{III}-E_{III}\approx 0.36$ MeV, agrees with experimetal data of Blons et al.
This is in a sharp contrast with the status of the IIIrd minima in
$^{232-236}$U: their experimental depth of $\geq3$ MeV contradicts all
realistic theoretical predictions. We emphasize the importance of repeating the
experiment on $^{232}$Th, by a technique similar to that used in the uranium
nuclei, for settling the puzzle of the third minima in actinides.
