| Kimberling Notation | Role | |
|---|---|---|
| 1 | X(1) Incenter | Perspector and Homothetic Center of the Euler Triangle of the Nagel Point and the Half-Median Triangle |
| 2 | X(2) Centroid | Perspector and Homothetic Center of the Euler Triangle of the Centroid and the Half-Median Triangle |
| 3 | X(3) Circumcenter | Perspector and Homothetic Center of the Euler Triangle of the Orthocenter and the Half-Median Triangle |
| 4 | X(4) Orthocenter | Perspector and Homothetic Center of the Euler Triangle of the de Longchamps Point and the Half-Median Triangle |
| 5 | X(5) Nine-Point Center | Perspector and Homothetic Center of the Euler Triangle of the Circumcenter and the Half-Median Triangle |
| 6 | X(6) Symmedian Point | Perspector and Homothetic Center of the Euler Triangle of the Retrocenter and the Half-Median Triangle |
| 7 | X(9) Mittenpunkt | Perspector and Homothetic Center of the Euler Triangle of the Gergonne Point and the Half-Median Triangle |
| 8 | X(10) Spieker Center | Perspector and Homothetic Center of the Euler Triangle of the Incenter and the Half-Median Triangle |
| 9 | X(11) Feuerbach Point | Perspector and Homothetic Center of the Euler Triangle of the Anticompliment of the Feuerbach Point and the Half-Median Triangle |
| 10 | X(37) Grinberg Point | Perspector and Homothetic Center of the Euler Triangle of the Moses Point and the Half-Median Triangle |
| 11 | X(39) Brocard Midpoint | Perspector and Homothetic Center of the Euler Triangle of the Third Brocard Point and the Half-Median Triangle |
| 12 | X(75) Moses Point | Perspector and Homothetic Center of the Euler Triangle of the Equal Parallelians Point and the Half-Median Triangle |
| 13 | X(114) | Perspector and Homothetic Center of the Euler Triangle of the Tarry Point and the Half-Median Triangle |
| 14 | X(115) Kiepert Center | Perspector and Homothetic Center of the Euler Triangle of the Steiner Point and the Half-Median Triangle |
| 15 | X(125) | Perspector and Homothetic Center of the Euler Triangle of the Euler Reflection Point and the Half-Median Triangle |
| 16 | X(126) | Perspector and Homothetic Center of the Euler Triangle of the Parry Point and the Half-Median Triangle |
| 17 | X(128) | Perspector and Homothetic Center of the Euler Triangle of the Gibert Point and the Half-Median Triangle |
| 18 | X(140) Nine-Point Center of the Medial Triangle | Perspector and Homothetic Center of the Euler Triangle of the Nine-Point Center and the Half-Median Triangle |
| 19 | X(141) Symmedian Point of the Medial Triangle | Perspector and Homothetic Center of the Euler Triangle of the Symmedian Point and the Half-Median Triangle |
| 20 | X(142) Mittenpunkt of the Medial Triangle | Perspector and Homothetic Center of the Euler Triangle of the Mittenpunkt and the Half-Median Triangle |
| 21 | X(216) | Perspector and Homothetic Center of the Euler Triangle of the Isotomic Conjugate of the Circumcenter and the Half-Median Triangle |
| 22 | X(427) | Perspector and Homothetic Center of the Euler Triangle of the Exeter Point and the Half-Median Triangle |
| 23 | X(442) | Perspector and Homothetic Center of the Euler Triangle of the Schiffler Point and the Half-Median Triangle |
| 24 | X(549) | Perspector and Homothetic Center of the Euler Triangle of the Center of the Orthocentroidal Circle and the Half-Median Triangle |
| 25 | X(618) | Perspector and Homothetic Center of the Euler Triangle of the Outer Fermat Point and the Half-Median Triangle |
| 26 | X(619) | Perspector and Homothetic Center of the Euler Triangle of the Inner Fermat Point and the Half-Median Triangle |
| 27 | X(620) | Perspector and Homothetic Center of the Euler Triangle of the Kiepert Center and the Half-Median Triangle |
| 28 | X(623) | Perspector and Homothetic Center of the Euler Triangle of the First Isodynamic Point and the Half-Median Triangle |
| 29 | X(624) | Perspector and Homothetic Center of the Euler Triangle of the Second Isodynamic Point and the Half-Median Triangle |
| 30 | X(625) | Perspector and Homothetic Center of the Euler Triangle of the Schoute Center and the Half-Median Triangle |
| 31 | X(626) | Perspector and Homothetic Center of the Euler Triangle of the Third Power Point and the Half-Median Triangle |
| 32 | X(629) | Perspector and Homothetic Center of the Euler Triangle of the Outer Napoleon Point and the Half-Median Triangle |
| 33 | X(630) | Perspector and Homothetic Center of the Euler Triangle of the Inner Napoleon Point and the Half-Median Triangle |
| 34 | X(639) | Perspector and Homothetic Center of the Euler Triangle of the First Kenmotu Point and the Half-Median Triangle |
| 35 | X(640) | Perspector and Homothetic Center of the Euler Triangle of the Second Kenmotu Point and the Half-Median Triangle |
| 36 | X(641) | Perspector and Homothetic Center of the Euler Triangle of the Outer Vecten Point and the Half-Median Triangle |
| 37 | X(642) | Perspector and Homothetic Center of the Euler Triangle of the Inner Vecten Point and the Half-Median Triangle |
| 38 | X(858) | Perspector and Homothetic Center of the Euler Triangle of the Far-Out Point and the Half-Median Triangle |
| 39 | X(946) | Perspector and Homothetic Center of the Euler Triangle of the Bevan Point and the Half-Median Triangle |
| 40 | X(993) | Perspector and Homothetic Center of the Euler Triangle of the Center of the Inner Johnson-Yff Circle and the Half-Median Triangle |
| 41 | X(1086) | Perspector and Homothetic Center of the Euler Triangle of the Yff Parabolic Point and the Half-Median Triangle |
| 42 | X(1125) | Perspector and Homothetic Center of the Euler Triangle of the Spieker Center and the Half-Median Triangle |
| 43 | X(1147) | Perspector and Homothetic Center of the Euler Triangle of the Prasolov Point and the Half-Median Triangle |
| 44 | X(1209) | Perspector and Homothetic Center of the Euler Triangle of the Kosnita Point and the Half-Median Triangle |
| 45 | X(1329) | Perspector and Homothetic Center of the Euler Triangle of the External Center of Similitude of the Incircle and the Circumcircle and the Half-Median Triangle |
| 46 | X(1385) | Perspector and Homothetic Center of the Euler Triangle of the Center of the Fuhrmann Circle and the Half-Median Triangle |
| 47 | X(2090) | Perspector and Homothetic Center of the Euler Triangle of the Yff Center of Conguence and the Half-Median Triangle |
| 48 | X(2886) | Perspector and Homothetic Center of the Euler Triangle of the Internal Center of Similitude of the Incircle and the Circumcircle and the Half-Median Triangle |
| 49 | X(2887) | Perspector and Homothetic Center of the Euler Triangle of the Second Power Point and the Half-Median Triangle |
| 50 | X(3035) | Perspector and Homothetic Center of the Euler Triangle of the Feuerbach Point and the Half-Median Triangle |
| 51 | X(3739) | Perspector and Homothetic Center of the Euler Triangle of the Grinberg Point and the Half-Median Triangle |
| 52 | X(3740) | Perspector and Homothetic Center of the Euler Triangle of the Weill Point and the Half-Median Triangle |
| 53 | X(3814) | Perspector and Homothetic Center of the Euler Triangle of the Inverse of the Incenter in the Circumcircle and the Half-Median Triangle |
| 54 | X(3934) | Perspector and Homothetic Center of the Euler Triangle of the Brocard Midpoint and the Half-Median Triangle |
| 55 | X(4885) | Perspector and Homothetic Center of the Euler Triangle of the Center of the Stevanovic Circle and the Half-Median Triangle |
| 56 | X(4999) | Perspector and Homothetic Center of the Euler Triangle of the Feuerbach Perspector and the Half-Median Triangle |
| 57 | X(5087) | Perspector and Homothetic Center of the Euler Triangle of the Schroder Point and the Half-Median Triangle |
| 58 | X(5123) | Perspector and Homothetic Center of the Euler Triangle of the Bevan-Schroder Point and the Half-Median Triangle |