It is sometimes confusing when jewelers talk about carats of diamonds and karats of gold. Carats of diamonds is simply a weight. karats of gold is actually a percentage of gold. We are going to talk about carats with a "C' which is a weight.
There arose a need to have parts of a carat so they came up with "Points" meaning one - one hundredth 1/100 of a carat. Points don't have anything to do with the way a stone is cut, it is simply a weight. For example 25 points (25/100) is one quarter of a Carat. Fifty points (50/100) a half carat.
Diamond cutters do not sit down and say, "let's cut half carats today". Master diamond cutters cut diamonds to waste as little as possible and yet yield the most brilliant diamonds. So you get 27 pointers and 51 pointers but very seldom exact half carats of quarter carats diamonds.
Keep in mind there is nothing magical about an exact half carat exact or an exact one carat. It is just a weight compared to a bean. The only reason for carats is to compare the relative size of gemstones.