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K696

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X(6), X(7), X(8), X(9), X(10), X(19), X(65), X(72), X(1193), X(1334), X(1400)

P1 = X(14624) = X(6)X(8) /\ X(10)X(1400) = X(42)-isoconjugate of X(1193)

P2 = X(14625) = X(6)X(7) /\ X(10)X(1334)

P3 = X(14626) = X(6)X(1334) /\ X(7)X(10) = X(42)-isoconjugate of P2

K696 is comparable to K382 since it also contains a good number of very common triangle centers, in particular 5 consecutive centers of the ETC Top 10.

K696 is nK(X42, X14594, X6) where X(14594) is the barycentric product X(190) x X(388) or X(664) x X(2345).

See also the related K697.

Collinearities on K696 :

X(42)-isoconjugates on K696 :

X(6), X(7), P2

X(6), X(8), P1

X(6), X(9), X(72)

X(6), X(19), X(65)

X(6), X(1193), X(1400)

X(6), X(1334), P3

X(7), X(8), X(65)

X(7), X(9), X(1400)

X(7), X(10), P3

X(8), X(9), X(1334)

X(8), X(10), X(1193)

X(9), X(10), X(19)

X(10), X(65), X(72)

X(10), X(1334), P2

X(10), X(1400), P1

X(65), X(1334), X(1400)

X(6), X(10)

X(7), X(1334)

X(8), X(1400)

X(9), X(65)

X(19), X(72)

X(1193), P1

P2, P3

The isogonal and isotomic transforms of K696 are also nKs passing respectively through :

• X(2), X(21), X(28), X(55), X(56), X(57), X(58), X(63), X(333), X(1220), X(1434)

• X(7), X(8), X(76), X(85), X(86), X(286), X(304), X(314), X(1240)

More generally, the Ω-isoconjugate of K696 is another nK. Here is a selection of such cubics containing at least nine ETC centers.

Ω = X(1) : X(7), X(9), X(27), X(57), X(69), X(75), X(81), X(314), X(333)
Ω = X(3) : X(69), X(77), X(81), X(219), X(222), X(326), X(332), X(1790), X(1812)
Ω = X(9) : X(1), X(2), X(21), X(29), X(200), X(274), X(312), X(345), X(1043)
Ω = X(31) : X(1), X(3), X(21), X(41), X(56), X(284), X(604), X(1014), X(1333), X(1474), X(2298)
Ω = X(32) : X(6), X(48), X(284), X(604), X(1397), X(1412), X(2175), X(2194), X(2203), X(2206)
Ω = X(37) : X(1), X(4), X(8), X(65), X(85), X(210), X(226), X(306), X(312), X(321)
Ω = X(41) : X(6), X(9), X(31), X(81), X(219), X(1253), X(2194), X(2287), X(2299), X(2328)
Ω = X(48) : X(58), X(63), X(212), X(222), X(283), X(394), X(603), X(1437), X(1791), X(1812)
Ω = X(55) : X(1), X(6), X(8), X(78), X(86), X(220), X(284), X(1043), X(1172), X(2287)
Ω = X(56) : X(6), X(7), X(77), X(81), X(86), X(269), X(1396), X(1407), X(1412)
Ω = X(58) : X(86), X(261), X(284), X(552), X(593), X(1014), X(1412), X(1444), X(2185)
Ω = X(65) : X(2), X(37), X(57), X(75), X(278), X(307), X(1088), X(1427), X(1441)
Ω = X(71) : X(1), X(3), X(73), X(78), X(306), X(345), X(348), X(1214), X(2318)
Ω = X(212) : X(3), X(48), X(78), X(284), X(1259), X(1444), X(1792), X(1802), X(2193), X(2327)
Ω = X(213) : X(9), X(25), X(31), X(37), X(55), X(57), X(71), X(1400), X(1402), X(2300)
Ω = X(284) : X(58), X(60), X(81), X(270), X(333), X(1098), X(1509), X(1812), X(2328)
Ω = X(604) : X(31), X(57), X(58), X(81), X(222), X(961), X(1106), X(1407), X(1408)
Ω = X(1333) : X(60), X(81), X(849), X(1408), X(1412), X(1790), X(2185), X(2194), X(2363)
Ω = X(1334) : X(2), X(33), X(37), X(42), X(55), X(200), X(346), X(2269), X(2321)
Ω = X(1400) : X(1), X(2), X(34), X(42), X(56), X(226), X(279), X(1042), X(1214), X(1427)
Ω = X(1402) : X(1), X(6), X(65), X(73), X(213), X(269), X(604), X(608), X(1042)
Ω = X(1824) : X(10), X(19), X(225), X(273), X(281), X(318), X(393), X(1829), X(1880)
Ω = X(1973) : X(6), X(19), X(608), X(1172), X(1395), X(1396), X(2203), X(2212), X(2299)
Ω = X(2333) : X(25), X(33), X(37), X(278), X(281), X(1096), X(1826), X(1880), X(2354)