Here is an easy way to model a brilliant cut gemstone.
This small tutorial is addressed primary to C4D users, but can be easily reconstructed in most other 3D programs.
The result will have no round girdle of course, but it's good enough for most uses.
As a base we choose a primitive cylinder with 8 rotation segments, 4 segments in height and 1 segment at caps.
Make it a polygon object by hitting "C" and call "Optimize" from Structure Menu. Now you can delete the Phong Tag and
follow the steps described in the picture. Use the blueprint below to find the correct proportions.
As a last step you can reduce the 8 triangles at the Table to 3 polygons by deleting the center point and creating 3 quads.