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Orthocubic

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Orthocubic

The orthocubic (or ortho cubic) Z(X_4) is a self-isogonal cubic with pivot point at the orthocenter H, so it has parameter x=cosBcosC and trilinear equation

cosBcosCalpha(beta^2-gamma^2)+cosCcosAbeta(gamma^2-alpha^2)+cosAcosBgamma(alpha^2-beta^2)=0

(Cundy and Parry 1995).

The orthocubic passes through the circumcenter O, orthocenter H, incenter I, excenters J_A, J_B, and J_C, and Kimberling centers X_(46), X_(90), X_(155), and X_(254) (Kimberling 1998, p. 240), as well as X_(371), X_(372), X_(485), X_(486), X_(487), and X_(488).

See also

Triangle Cubic

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References

Cundy, H. M. and Parry, C. F. "Some Cubic Curves Associated with a Triangle." J. Geom. 53, 41-66, 1995.Gibert, B. "Orthocubic." http://perso.wanadoo.fr/bernard.gibert/Exemples/k006.html.Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.

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Orthocubic

Cite this as:

Weisstein, Eric W. "Orthocubic." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Orthocubic.html

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