The number of facets on a diamond stone are not considered when valuing a diamond.
The smooth surface areas of a diamond that have been cut, polished and positioned are called facets. They allow light to enter and reflect back which gives it the brilliance, fire, sparkle and luster of a diamond. The number of facets a brilliant cut round diamond has is 58.If you add more facets to the crown you are actually compressing more facets into the same area and by doing so they would have to be smaller. Smaller facets mean smaller windows and less light. So having more extra facets isn’t a good idea.
Facets are not part of how a diamond is priced. A diamond is priced by its carat weight, its clarity, its cut and its colour.
The edges of facets -- where facets meet would be called by a geometric name: angle. You can read more about the names of cuts and their component faces/ facets, below.
Diamonds sparkle according to the refractive angles cut into the stone. A single-cut diamond has 17 facets; common round cuts today have more than 50 facets. There's no question that a single-cut diamond will sparkle, but it might not sparkle as much as a diamond of the same weight with more facets cut into it.
The links in the chain has facets like a diamond so that it sparkles more.
Emerald cut diamonds generally have between 50 and 58 facets. You can find more about diamonds from the Gemological Institute of America. That's how I learned all of my diamond info. gia4s.gia.edu.
From Diamond Source: "A cushion cut is a square or squarish-rectangular cut with rounded corners and 58 brilliant-style facets that resemble a pillow shape..." You can read more about this cut, below.
If there is a tip, it is called culet. Some diamond cuts have no 'tip' or point.You can read more about facets of diamonds and their names, below.
Depending on how the pavilion is designed, the princess cut diamond can have more facets than the standard round brilliant. Some have just 50 facets, while others range to 144 facets. The amount of sparkle can hide flaws in clarity and cut, to some degree. However, no cut will hide color -- in fact, you can find the true colour in the corners of a princess cut.
The Asscher cut may vary in the number of facets, depending on the weight of the stone, who cut the stone and who is selling it. This cut is essentially a square emerald cut. You can read more about it, below.
Depending on how the pavilion is designed, the princess cut diamond can have more facets than the standard round brilliant. Some have just 50 facets, while others range to 144 facets. The amount of sparkle can hide flaws in clarity and cut, to some degree. However, no cut will hide color -- in fact, you can find the true colour in the corners of a princess cut.
Because you chose diamonds as the category for your question, one can assume that your question might also be 'Who invents the angles and placement of facets for a new diamond cut?' From the link, below, you can see how a diamond's facets are angled, so that light can bounce most effectively through the stone, from facet to facet. This is essentially a geometric puzzle that a gemologist can solve when planning the cut of a particular stone. Over time, with the development of more precise cutting tools, gemologists have been better able to solve and re-solve this geometric puzzle, thus leading to new cut patterns for diamonds.