| Role | Kimberling Notation | |
|---|---|---|
| 1 | Perspector and Homothetic Center of the Euler Triangle of the Incenter and the Medial Triangle | X(1125) |
| 2 | Perspector and Homothetic Center of the Euler Triangle of the Centroid and the Medial Triangle | X(2) Centroid |
| 3 | Perspector and Homothetic Center of the Euler Triangle of the Circumcenter and the Medial Triangle | X(140) Nine-Point Center of the Medial Triangle |
| 4 | Perspector and Homothetic Center of the Euler Triangle of the Orthocenter and the Medial Triangle | X(5) Nine-Point Center |
| 5 | Perspector and Homothetic Center of the Euler Triangle of the Nine-Point Center and the Medial Triangle | X(3628) |
| 6 | Perspector and Homothetic Center of the Euler Triangle of the Symmedian Point and the Medial Triangle | X(3589) |
| 7 | Perspector and Homothetic Center of the Euler Triangle of the Gergonne Point and the Medial Triangle | X(142) Mittenpunkt of the Medial Triangle |
| 8 | Perspector and Homothetic Center of the Euler Triangle of the Nagel Point and the Medial Triangle | X(10) Spieker Center |
| 9 | Perspector and Homothetic Center of the Euler Triangle of the Spieker Center and the Medial Triangle | X(3634) |
| 10 | Perspector and Homothetic Center of the Euler Triangle of the de Longchamps Point and the Medial Triangle | X(3) Circumcenter |
| 11 | Perspector and Homothetic Center of the Euler Triangle of the Far-Out Point and the Medial Triangle | X(468) |
| 12 | Perspector and Homothetic Center of the Euler Triangle of the Grinberg Point and the Medial Triangle | X(4698) |
| 13 | Perspector and Homothetic Center of the Euler Triangle of the Prasolov Point and the Medial Triangle | X(5449) |
| 14 | Perspector and Homothetic Center of the Euler Triangle of the Retrocenter and the Medial Triangle | X(141) Symmedian Point of the Medial Triangle |
| 15 | Perspector and Homothetic Center of the Euler Triangle of the Moses Point and the Medial Triangle | X(3739) |
| 16 | Perspector and Homothetic Center of the Euler Triangle of the Third Brocard Point and the Medial Triangle | X(3934) |
| 17 | Perspector and Homothetic Center of the Euler Triangle of the Steiner Point and the Medial Triangle | X(620) |
| 18 | Perspector and Homothetic Center of the Euler Triangle of the Anticompliment of the Feuerbach Point and the Medial Triangle | X(3035) |
| 19 | Perspector and Homothetic Center of the Euler Triangle of the Yff Parabolic Point and the Medial Triangle | X(4422) |
| 20 | Perspector and Homothetic Center of the Euler Triangle of the Equal Parallelians Point and the Medial Triangle | X(37) Grinberg Point |
| 21 | Perspector and Homothetic Center of the Euler Triangle of the Weill Point and the Medial Triangle | X(3848) |
| 22 | Perspector and Homothetic Center of the Euler Triangle of the Center of the Orthocentroidal Circle and the Medial Triangle | X(547) |
| 23 | Perspector and Homothetic Center of the Euler Triangle of the Center of the Inner Johnson-Yff Circle and the Medial Triangle | X(3822) |
| 24 | Perspector and Homothetic Center of the Euler Triangle of the Center of the Outer Johnson-Yff Circle and the Medial Triangle | X(3825) |