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