with the Affine grid
This time the points are generated by the orthocenter-incenter combination and there is a lot more information. The coordinates, names used in the Triangle Book, and Kimberling numbers are given. In addition I drew a grid, which I call the affine grid, and which places the position of these points. The coordinates show the pattern of organization of these points. They are the orbits of a group that Kimberling proposed in his first article 10 years ago using the X numbers.