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Any isogonal cubic is invariant under isogonal conjugation. If K is a non-isogonal circum-cubic, its isogonal transform is another circum-cubic K'.

When K = pK(X2,P), we have K' = pK(X32,Q) where Q is the isogonal conjugate of the isotomic conjugate of P.

P

K

Q

K'

X(69)

K007 Lucas cubic

X(3)

K172

X(316)

K008 Droussent cubic, circular cubic

X(23)

K108

X(75)

K034 Spieker perspector cubic

X(1)

K175

X(264)

K045 Euler perspector cubic

X(4)

K176

E(371)

K092, a pK60

 

 

X(309)

K133

X(84)

K180

X(76)

K141

X(2)

K177

X(3)

K146

X(184)

 

X(322)

K154

X(40)

K179

X(4)

K170

X(25)

K171

X(8)

K200

X(55)

 

tgX(20)

K235

X(20)

K236

X(892)

K240

X(691)

 

X(99)

K242

X(110)

 

X(314)

K254

X(21)

 

X(298)

K264a

X(15)

 

X(299)

K264b

X(16)

 

tX(74)

K279

X(30)

 

X(320)

K311

X(36)

K312

X(22)

 

X(206)

K160

X(315)

 

X(22)

K174

X(305)

 

X(69)

K178

 

 

 

 

 

 

 

 

Other cubics

K

K'

K009 Lemoine cubic

K028 Musselman (third) cubic

K010 Simson cubic

K162 cK(#X6, X3)

K015 Tucker nodal cubic

K229 nK(X32, X6, X6)

K039 Jerabek strophoid

K025 Ehrmann strophoid

K043 Droussent medial cubic

K273 pK(X111,X671)

K060 Kn = O(X5) orthopivotal

K073 Ki

K135 pK(X1911, X291)

K251 pK(X238, X2)

K155 pK(X31, X238)

K323 pK(X1, X239)

K167 pK(X184, X6)

K181 pK(X4, X4)

K184 pK(X76, X76)

K346 pK(X1501, X6)

K185 nK0(X2, X523)

K222 nK0(X32, X512)

K199 Soddy-Nagel cubic

K632 pK(X604, X1)

K229 nK(X32, X6, X6)

K015 nK(X2, X2, X2)

K233 pK(X25, X4)

K168 pK(X3, X2)

K261a O(X62) orthopivotal

K261b O(X61) orthopivotal

K262a O(X15) orthopivotal

K262b O(X16) orthopivotal

K263 O(X511) orthopivotal

K292 O(X182) orthopivotal

K278 pK(X1989, X1989)

pK(X50, X6)

K290 O(X39) orthopivotal

K291 O(X32) orthopivotal

K308 pK(X1, X8)

pK(X31, X9)

K317 pK(X81, X86)

K362 pK(X213, X1)

K319 pK(X1333, X81)

K345 pK(X37, X2)