Coplanar points are points that lie on the same geometric plane. By definition, three points define a plane, and for any three points, a plane exists that all three points lie on. Since a plane is infinite, the number of possible coplanar points for any plane is also infinite.
A plane is a two-dimensional surface, and any shape, such a polygon, a curve or a straight line, that can be drawn in two dimensions is made up of coplanar points. Points can lie in more than one plane at a time if those planes intersect. If two distinct planes do intersect, they intersect along a single straight line.