Classic centers (incenter, centroid, circumcenter,
orthocenter and nine-point-center) of most of triangles defined in Wolfram’s has
been calculated. Below table shows their indexes in ETC.
For centers in yellow (not in ETC), please download
table with barycentric coordinates, some properties and ETC-6-9-13 search values
from the next link:
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Incenter
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Centroid
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Circumcenter
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Orthocenter
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NPC
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ABC
|
X(1)
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X(2)
|
X(3)
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X(4)
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X(5)
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ANTICOMPLEMENTARY
|
X(8)
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X(2)
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X(4)
|
X(20)
|
X(3)
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|
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BROCARD 1
|
X(3923)
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X(2)
|
X(182)
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X(1352)
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BROCARD 2
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X(182)
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|
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BROCARD 3
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|
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|
|
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BROCARD 4
|
|
X(6032)
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X(381)
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CIRCUMMEDIAL
|
|
|
X(3)
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|
|
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CICUMNORMAL
|
X(3)
|
X(3)
|
X(3)
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X(3)
|
X(3)
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|
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CIRCUMORTHIC
|
X(4)
|
X(5890)
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X(3)
|
X(5889)
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X(6102)
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CIRCUMPERP 1
|
|
X(165)
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X(3)
|
X(40)
|
X(3579)
|
|
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CIRCUMPERP 2
|
|
X(3576)
|
X(3)
|
X(1)
|
X(1385)
|
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COSYMMEDIAL
|
|
X(353)
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X(3)
|
|
|
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EULER
|
X(946)
|
X(381)
|
X(5)
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X(4)
|
X(546)
|
|
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EXCENTRAL
|
X(164)
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X(165)
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X(40)
|
X(1)
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X(3)
|
|
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EXTANGENTS
|
X(40)
|
|
|
X(6237)
|
|
|
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EXTOUCH
|
|
X(210)
|
X(1158)
|
|
|
|
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FEUERBACH
|
X(5960)
|
X(5947)
|
X(5)
|
X(5948)
|
|
|
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FUHRMANN
|
|
X(5587)
|
X(355)
|
X(1)
|
X(5)
|
|
|
GREBE OUTER
|
X(3640)
|
X(5860)
|
X(1160)
|
X(5870)
|
X(5874)
|
|
|
GREBE INNER
|
X(3641)
|
X(5861)
|
X(1161)
|
X(5871)
|
X(5875)
|
|
|
HEXYL
|
|
X(3576)
|
X(1)
|
X(40)
|
X(3)
|
|
|
INCENTRAL
|
|
X(1962)
|
|
X(500)
|
|
|
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INTANGENTS
|
X(1)
|
|
|
X(6238)
|
|
|
|
INTOUCH
|
X(177)
|
X(354)
|
X(1)
|
X(65)
|
X(942)
|
|
|
JOHNSON
|
X(355)
|
X(381)
|
X(4)
|
X(3)
|
X(5)
|
|
|
LEMOINE
|
|
|
|
|
|
|
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LUCAS CENTRAL
|
X(1151)
|
|
|
|
|
|
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LUCAS TANGENTS
|
|
|
X(1151)
|
|
|
|
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MACBEATH
|
|
|
|
|
|
|
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MEDIAL
|
X(10)
|
X(2)
|
X(5)
|
X(3)
|
X(140)
|
|
|
MIDARC
|
|
X(3576)
|
X(3)
|
X(1)
|
X(1385)
|
|
|
MIDHEIGHT
|
|
X(5943)
|
X(5893)
|
|
|
|
|
MIXTILINEAR
|
|
|
|
|
|
|
|
MORLEY 1
|
X(356)
|
X(356)
|
X(356)
|
X(356)
|
X(356)
|
|
|
MORLEY 2
|
X(3276)
|
X(3276)
|
X(3276)
|
X(3276)
|
X(3276)
|
|
|
MORLEY 3
|
X(3277)
|
X(3277)
|
X(3277)
|
X(3277)
|
X(3277)
|
|
|
NAPOLEON INNER
|
X(2)
|
X(2)
|
X(2)
|
X(2)
|
X(2)
|
|
|
NAPOLEON OUTER
|
X(2)
|
X(2)
|
X(2)
|
X(2)
|
X(2)
|
|
|
NEUBERG 1
|
|
X(2)
|
|
|
|
|
|
NEUBERG 2
|
|
X(2)
|
|
|
|
|
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ORTHIC
|
X(4)
|
X(51)
|
X(5)
|
X(52)
|
X(143)
|
|
|
ORTHOCENTROIDAL
|
X(5902)
|
X(5640)
|
X(381)
|
X(5890)
|
X(5946)
|
|
|
REFLECTION
|
|
X(3060)
|
X(195)
|
|
|
|
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SQUARES OUTER
|
|
|
|
|
|
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SQUARES INNER
|
|
|
|
|
|
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STEINER
|
|
|
|
X(3)
|
|
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SYMMEDIAL
|
|
|
|
|
|
|
|
TANGENTIAL
|
X(3)
|
X(154)
|
X(26)
|
X(155)
|
X(156)
|
|
|
VECTEN OUTER
|
|
X(2)
|
X(641)
|
X(485)
|
X(6118)
|
|
|
VECTEN INNER
|
|
X(2)
|
X(642)
|
X(486)
|
X(6119)
|
|
|
YFF CONTACT
|
|
|
X(5592)
|
X(8)
|
|
|
