Table P-X
Harmonic Conjugates.
Points available at the Kimberling's Encyclopedia ETC.
The ETC version: The 8998 points version of 2015.
The "Discoverer" database version: October 2013.
Last update: 2016-03-21

      Role     Kimberling Notation  
  1     Harmonic Conjugate of the X(01) Incenter with respect to the X(02) Centroid and the X(08) Nagel Point (the X(01) Incenter is not between the X(02) Centroid and X(08) Nagel Point)     X(10)   Spieker Center  
  2     Harmonic Conjugate of the X(01) Incenter with respect to the X(02) Centroid and the X(10) Spieker Center (the X(01) Incenter is not between the X(02) Centroid and X(10) Spieker Center)     X(1698)    
  3     Harmonic Conjugate of the X(01) Incenter with respect to the X(05) Nine-Point Center and the X(11) Feuerbach Point (the X(01) Incenter is between the X(05) Nine-Point Center and X(11) Feuerbach Point)     X(7741)    
  4     Harmonic Conjugate of the X(01) Incenter with respect to the X(05) Nine-Point Center and the X(12) Feuerbach Perspector (the X(01) Incenter is not between the X(05) Nine-Point Center and X(12) Feuerbach Perspector)     X(7951)    
  5     Harmonic Conjugate of the X(01) Incenter with respect to the X(06) Symmedian Point and the X(09) Mittenpunkt (the X(01) Incenter is between the X(06) Symmedian Point and X(09) Mittenpunkt)     X(1743)    
  6     Harmonic Conjugate of the X(01) Incenter with respect to the X(07) Gergonne Point and the X(20) de Longchamps Point (the X(01) Incenter is between the X(07) Gergonne Point and X(20) de Longchamps Point)     X(4292)    
  7     Harmonic Conjugate of the X(01) Incenter with respect to the X(08) Nagel Point and the X(10) Spieker Center (the X(01) Incenter is not between the X(08) Nagel Point and X(10) Spieker Center)     X(3679)    
  8     Harmonic Conjugate of the X(01) Incenter with respect to the X(11) Feuerbach Point and the X(12) Feuerbach Perspector (the X(01) Incenter is between the X(11) Feuerbach Point and X(12) Feuerbach Perspector)     X(5)   Nine-Point Center  
  9     Harmonic Conjugate of the X(02) Centroid with respect to the X(01) Incenter and the X(08) Nagel Point (the X(02) Centroid is between the X(01) Incenter and X(08) Nagel Point)     X(145)   Nagel Point of the Anticomplementary Triangle  
  10     Harmonic Conjugate of the X(02) Centroid with respect to the X(01) Incenter and the X(10) Spieker Center (the X(02) Centroid is between the X(01) Incenter and X(10) Spieker Center)     X(8)   Nagel Point  
  11     Harmonic Conjugate of the X(02) Centroid with respect to the X(03) Circumcenter and the X(04) Orthocenter (the X(02) Centroid is between the X(03) Circumcenter and X(04) Orthocenter)     X(20)   de Longchamps Point  
  12     Harmonic Conjugate of the X(02) Centroid with respect to the X(03) Circumcenter and the X(05) Nine-Point Center (the X(02) Centroid is between the X(03) Circumcenter and X(05) Nine-Point Center)     X(4)   Orthocenter  
  13     Harmonic Conjugate of the X(02) Centroid with respect to the X(03) Circumcenter and the X(20) de Longchamps Point (the X(02) Centroid is not between the X(03) Circumcenter and X(20) de Longchamps Point)     X(3522)    
  14     Harmonic Conjugate of the X(02) Centroid with respect to the X(04) Orthocenter and the X(05) Nine-Point Center (the X(02) Centroid is not between the X(04) Orthocenter and X(05) Nine-Point Center)     X(3091)    
  15     Harmonic Conjugate of the X(02) Centroid with respect to the X(04) Orthocenter and the X(20) de Longchamps Point (the X(02) Centroid is between the X(04) Orthocenter and X(20) de Longchamps Point)     X(3146)    
  16     Harmonic Conjugate of the X(02) Centroid with respect to the X(05) Nine-Point Center and the X(20) de Longchamps Point (the X(02) Centroid is between the X(05) Nine-Point Center and X(20) de Longchamps Point)     X(3832)    
  17     Harmonic Conjugate of the X(02) Centroid with respect to the X(07) Gergonne Point and the X(09) Mittenpunkt (the X(02) Centroid is between the X(07) Gergonne Point and X(09) Mittenpunkt)     X(144)   Gergonne Point of the Anticomplementary Triangle  
  18     Harmonic Conjugate of the X(02) Centroid with respect to the X(08) Nagel Point and the X(10) Spieker Center (the X(02) Centroid is not between the X(08) Nagel Point and X(10) Spieker Center)     X(3617)    
  19     Harmonic Conjugate of the X(03) Circumcenter with respect to the X(02) Centroid and the X(04) Orthocenter (the X(03) Circumcenter is not between the X(02) Centroid and X(04) Orthocenter)     X(5)   Nine-Point Center  
  20     Harmonic Conjugate of the X(03) Circumcenter with respect to the X(02) Centroid and the X(05) Nine-Point Center (the X(03) Circumcenter is not between the X(02) Centroid and X(05) Nine-Point Center)     X(1656)    
  21     Harmonic Conjugate of the X(03) Circumcenter with respect to the X(02) Centroid and the X(20) de Longchamps Point (the X(03) Circumcenter is between the X(02) Centroid and X(20) de Longchamps Point)     X(4)   Orthocenter  
  22     Harmonic Conjugate of the X(03) Circumcenter with respect to the X(04) Orthocenter and the X(05) Nine-Point Center (the X(03) Circumcenter is not between the X(04) Orthocenter and X(05) Nine-Point Center)     X(381)   Center of the Orthocentroidal Circle  
  23     Harmonic Conjugate of the X(03) Circumcenter with respect to the X(05) Nine-Point Center and the X(20) de Longchamps Point (the X(03) Circumcenter is between the X(05) Nine-Point Center and X(20) de Longchamps Point)     X(382)    
  24     Harmonic Conjugate of the X(03) Circumcenter with respect to the X(15) First Isodynamic Point and the X(16) Second Isodynamic Point (the X(03) Circumcenter is not between the X(15) First Isodynamic Point and X(16) Second Isodynamic Point)     X(6)   Symmedian Point  
  25     Harmonic Conjugate of the X(04) Orthocenter with respect to the X(02) Centroid and the X(03) Circumcenter (the X(04) Orthocenter is not between the X(02) Centroid and X(03) Circumcenter)     X(631)    
  26     Harmonic Conjugate of the X(04) Orthocenter with respect to the X(02) Centroid and the X(05) Nine-Point Center (the X(04) Orthocenter is not between the X(02) Centroid and X(05) Nine-Point Center)     X(3090)    
  27     Harmonic Conjugate of the X(04) Orthocenter with respect to the X(02) Centroid and the X(20) de Longchamps Point (the X(04) Orthocenter is not between the X(02) Centroid and X(20) de Longchamps Point)     X(3)   Circumcenter  
  28     Harmonic Conjugate of the X(04) Orthocenter with respect to the X(03) Circumcenter and the X(05) Nine-Point Center (the X(04) Orthocenter is not between the X(03) Circumcenter and X(05) Nine-Point Center)     X(2)   Centroid  
  29     Harmonic Conjugate of the X(04) Orthocenter with respect to the X(03) Circumcenter and the X(20) de Longchamps Point (the X(04) Orthocenter is not between the X(03) Circumcenter and X(20) de Longchamps Point)     X(376)    
  30     Harmonic Conjugate of the X(04) Orthocenter with respect to the X(05) Nine-Point Center and the X(20) de Longchamps Point (the X(04) Orthocenter is not between the X(05) Nine-Point Center and X(20) de Longchamps Point)     X(631)    
  31     Harmonic Conjugate of the X(05) Nine-Point Center with respect to the X(01) Incenter and the X(11) Feuerbach Point (the X(05) Nine-Point Center is not between the X(01) Incenter and X(11) Feuerbach Point)     X(496)   Harmonic Conjugate of the Johnson Midpoint  
  32     Harmonic Conjugate of the X(05) Nine-Point Center with respect to the X(01) Incenter and the X(12) Feuerbach Perspector (the X(05) Nine-Point Center is not between the X(01) Incenter and X(12) Feuerbach Perspector)     X(495)   Johnson Midpoint  
  33     Harmonic Conjugate of the X(05) Nine-Point Center with respect to the X(02) Centroid and the X(03) Circumcenter (the X(05) Nine-Point Center is not between the X(02) Centroid and X(03) Circumcenter)     X(140)   Nine-Point Center of the Medial Triangle  
  34     Harmonic Conjugate of the X(05) Nine-Point Center with respect to the X(02) Centroid and the X(04) Orthocenter (the X(05) Nine-Point Center is between the X(02) Centroid and X(04) Orthocenter)     X(3)   Circumcenter  
  35     Harmonic Conjugate of the X(05) Nine-Point Center with respect to the X(02) Centroid and the X(20) de Longchamps Point (the X(05) Nine-Point Center is not between the X(02) Centroid and X(20) de Longchamps Point)     X(631)    
  36     Harmonic Conjugate of the X(05) Nine-Point Center with respect to the X(03) Circumcenter and the X(20) de Longchamps Point (the X(05) Nine-Point Center is not between the X(03) Circumcenter and X(20) de Longchamps Point)     X(548)    
  37     Harmonic Conjugate of the X(05) Nine-Point Center with respect to the X(04) Orthocenter and the X(20) de Longchamps Point (the X(05) Nine-Point Center is between the X(04) Orthocenter and X(20) de Longchamps Point)     X(382)    
  38     Harmonic Conjugate of the X(05) Nine-Point Center with respect to the X(11) Feuerbach Point and the X(12) Feuerbach Perspector (the X(05) Nine-Point Center is not between the X(11) Feuerbach Point and X(12) Feuerbach Perspector)     X(1)   Incenter  
  39     Harmonic Conjugate of the X(05) Nine-Point Center with respect to the X(13) Outer Fermat Point and the X(18) Inner Napoleon Point (the X(05) Nine-Point Center is not between the X(13) Outer Fermat Point and X(18) Inner Napoleon Point)     X(62)   Isogonal Conjugate of the Inner Napoleon Point  
  40     Harmonic Conjugate of the X(05) Nine-Point Center with respect to the X(14) Inner Fermat Point and the X(17) Outer Napoleon Point (the X(05) Nine-Point Center is not between the X(14) Inner Fermat Point and X(17) Outer Napoleon Point)     X(61)   Isogonal Conjugate of the Outer Napoleon Point  
  41     Harmonic Conjugate of the X(06) Symmedian Point with respect to the X(01) Incenter and the X(09) Mittenpunkt (the X(06) Symmedian Point is not between the X(01) Incenter and X(09) Mittenpunkt)     X(37)   Grinberg Point  
  42     Harmonic Conjugate of the X(06) Symmedian Point with respect to the X(13) Outer Fermat Point and the X(14) Inner Fermat Point (the X(06) Symmedian Point is between the X(13) Outer Fermat Point and X(14) Inner Fermat Point)     X(381)   Center of the Orthocentroidal Circle  
  43     Harmonic Conjugate of the X(06) Symmedian Point with respect to the X(15) First Isodynamic Point and the X(16) Second Isodynamic Point (the X(06) Symmedian Point is between the X(15) First Isodynamic Point and X(16) Second Isodynamic Point)     X(3)   Circumcenter  
  44     Harmonic Conjugate of the X(06) Symmedian Point with respect to the X(17) Outer Napoleon Point and the X(18) Inner Napoleon Point (the X(06) Symmedian Point is between the X(17) Outer Napoleon Point and X(18) Inner Napoleon Point)     X(1656)    
  45     Harmonic Conjugate of the X(07) Gergonne Point with respect to the X(01) Incenter and the X(20) de Longchamps Point (the X(07) Gergonne Point is not between the X(01) Incenter and X(20) de Longchamps Point)     X(4313)    
  46     Harmonic Conjugate of the X(08) Nagel Point with respect to the X(01) Incenter and the X(02) Centroid (the X(08) Nagel Point is not between the X(01) Incenter and X(02) Centroid)     X(3616)    
  47     Harmonic Conjugate of the X(08) Nagel Point with respect to the X(01) Incenter and the X(10) Spieker Center (the X(08) Nagel Point is not between the X(01) Incenter and X(10) Spieker Center)     X(2)   Centroid  
  48     Harmonic Conjugate of the X(08) Nagel Point with respect to the X(02) Centroid and the X(10) Spieker Center (the X(08) Nagel Point is not between the X(02) Centroid and X(10) Spieker Center)     X(667)    
  49     Harmonic Conjugate of the X(09) Mittenpunkt with respect to the X(01) Incenter and the X(06) Symmedian Point (the X(09) Mittenpunkt is not between the X(01) Incenter and X(06) Symmedian Point)     X(1449)    
  50     Harmonic Conjugate of the X(09) Mittenpunkt with respect to the X(02) Centroid and the X(07) Gergonne Point (the X(09) Mittenpunkt is not between the X(02) Centroid and X(07) Gergonne Point)     X(142)   Mittenpunkt of the Medial Triangle  
  51     Harmonic Conjugate of the X(10) Spieker Center with respect to the X(01) Incenter and the X(02) Centroid (the X(10) Spieker Center is not between the X(01) Incenter and X(02) Centroid)     X(1125)    
  52     Harmonic Conjugate of the X(10) Spieker Center with respect to the X(02) Centroid and the X(08) Nagel Point (the X(10) Spieker Center is between the X(02) Centroid and X(08) Nagel Point)     X(1)   Incenter  
  53     Harmonic Conjugate of the X(11) Feuerbach Point with respect to the X(01) Incenter and the X(05) Nine-Point Center (the X(11) Feuerbach Point is not between the X(01) Incenter and X(05) Nine-Point Center)     X(12)   Feuerbach Perspector  
  54     Harmonic Conjugate of the X(11) Feuerbach Point with respect to the X(05) Nine-Point Center and the X(12) Feuerbach Perspector (the X(11) Feuerbach Point is not between the X(05) Nine-Point Center and X(12) Feuerbach Perspector)     X(3614)    
  55     Harmonic Conjugate of the X(12) Feuerbach Perspector with respect to the X(01) Incenter and the X(05) Nine-Point Center (the X(12) Feuerbach Perspector is between the X(01) Incenter and X(05) Nine-Point Center)     X(11)   Feuerbach Point  
  56     Harmonic Conjugate of the X(12) Feuerbach Perspector with respect to the X(05) Nine-Point Center and the X(11) Feuerbach Point (the X(12) Feuerbach Perspector is between the X(05) Nine-Point Center and X(11) Feuerbach Point)     X(7173)    
  57     Harmonic Conjugate of the X(15) First Isodynamic Point with respect to the X(03) Circumcenter and the X(06) Symmedian Point (the X(15) First Isodynamic Point is between the X(03) Circumcenter and X(06) Symmedian Point)     X(16)   Second Isodynamic Point  
  58     Harmonic Conjugate of the X(15) First Isodynamic Point with respect to the X(06) Symmedian Point and the X(16) Second Isodynamic Point (the X(15) First Isodynamic Point is not between the X(06) Symmedian Point and X(16) Second Isodynamic Point)     X(62)   Isogonal Conjugate of the Inner Napoleon Point  
  59     Harmonic Conjugate of the X(16) Second Isodynamic Point with respect to the X(03) Circumcenter and the X(06) Symmedian Point (the X(16) Second Isodynamic Point is not between the X(03) Circumcenter and X(06) Symmedian Point)     X(15)   First Isodynamic Point  
  60     Harmonic Conjugate of the X(16) Second Isodynamic Point with respect to the X(06) Symmedian Point and the X(15) First Isodynamic Point (the X(16) Second Isodynamic Point is not between the X(06) Symmedian Point and X(15) First Isodynamic Point)     X(61)   Isogonal Conjugate of the Outer Napoleon Point  
  61     Harmonic Conjugate of the X(20) de Longchamps Point with respect to the X(02) Centroid and the X(03) Circumcenter (the X(20) de Longchamps Point is not between the X(02) Centroid and X(03) Circumcenter)     X(3523)    
  62     Harmonic Conjugate of the X(20) de Longchamps Point with respect to the X(02) Centroid and the X(04) Orthocenter (the X(20) de Longchamps Point is not between the X(02) Centroid and X(04) Orthocenter)     X(3091)    
  63     Harmonic Conjugate of the X(20) de Longchamps Point with respect to the X(02) Centroid and the X(05) Nine-Point Center (the X(20) de Longchamps Point is not between the X(02) Centroid and X(05) Nine-Point Center)     X(7486)    
  64     Harmonic Conjugate of the X(20) de Longchamps Point with respect to the X(03) Circumcenter and the X(04) Orthocenter (the X(20) de Longchamps Point is not between the X(03) Circumcenter and X(04) Orthocenter)     X(2)   Centroid  
  65     Harmonic Conjugate of the X(20) de Longchamps Point with respect to the X(03) Circumcenter and the X(05) Nine-Point Center (the X(20) de Longchamps Point is not between the X(03) Circumcenter and X(05) Nine-Point Center)     X(631)    
  66     Harmonic Conjugate of the X(20) de Longchamps Point with respect to the X(04) Orthocenter and the X(05) Nine-Point Center (the X(20) de Longchamps Point is not between the X(04) Orthocenter and X(05) Nine-Point Center)     X(3832)