Why are there so many different shapes of segments?
When grinding concrete the perimeter or edge of the segment cuts the concrete rather than the middle part of the segment grinding the concrete. For this reason, if you have a shape like a circle. It would have the smallest perimeter for the area. And if you have a star shape that may have a larger perimeter for the total surface area of the segment.
There are generally 2 reasons why you may grind a concrete floor. Either for the purpose of polishing the floor or for preparation of a coating.
If you are going to polish the concrete floor each stage you are simply removing the scratched from the previous grinding pass.
Hexagon. Husqvarna have a hexagon
Zig Zag. A person has a patent on this shape.