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Orthocubic

Definition

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 = cos B cos C and trilinear equation cos B cos C α(β^2 - γ^2) + cos C cos A β(γ^2 - α^2) + cos A cos B γ(α^2 - β^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, as well as X_371, X_372, X_485, X_486, X_487, and X_488.

Related term

triangle cubic

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