You can learn more about fantasy cuts here.
The first part of the fantasy cutting process is to cut a finished stone. The second part is to carve it. Typically, freeforms are used. Although the stone is a freeform, the techniques are the same as faceting any other stone.
Cutting A Fantasy Gemstone Pavilion
Start with the pavilion.
Determine where the table will be placed and grind a flat for dopping as shown below.
It’s nice to note that most fantasy gemstones are freeforms. This allows you to use all your rough and maximize yield. In this case, I used a 96-index gear. For demonstration purposes, I used both standard flat facets and a curved facet. The curve was cut by freewheeling the index gear and grinding it to a pleasantly shaped curve.
For your first attempt, stick to all flats. (Curves are…