The cabochon cut is not really a facet cut. It has rounded sides.
The cabochon cut is a very old cut/grind.
The sugarloaf is a "square" rounded pyrimidal cut/grind.
Some lapidarist cut a square facet design, and then grind off to rounded sides.
The work is done by hand, so there are many possible designs.
Your picture shows grooves cut, for the mounting. This is not always done, if another mounting can work.
The bottom can be round or flat, below the "girdle".
It seems easy enough to boolean together some dome shapes in MoI, to make the rounded sides. Plus some fillets.
