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