With respect, paraphrasing the Bible: "And so from this one triangle, came descendants as numerous as the stars in the sky and as countless as the sand on the seashore." - Hebrews 11:12
This dynamic sketch displays the first 360 points listed in Clark Kimberling's Encyclopedia of Triangle Centers - ETC plus the two so-called De Villiers points. The following points are enlarged & labelled in the sketch with their ETC labels:
1 = incentre
2 = centroid
3 = circumcentre
4 = orthocentre
1127 = 1st De Villiers point
1128 = 2nd De Villiers point.
Note: Currently, there are over 7 000 special triangle points listed in the ETC, and the list keeps growing. For more about these various triangle centres, and their properties, go to the link above.
360 Encyclopedia of Triangle Centres
Go to De Villiers points for more information about these particular points, as well as a dynamic sketch illustrating the location (construction) of these points.
Download a zipped Sketchpad file of the above dynamic sketch here, which also displays the barycentric coordinates of each point.
By Michael de Villiers. Created with WebSketchpad, 28 June 2022.