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too complicated to be written here. Click on the link to download a text file. 

H3 : ∑ a^2 (v + w) / (v  w) = 0 (1) aH3 : ∑ a^2 u / (v  w) = 0 (2) meaning that the line u x + v y + w z = 0 is tangent to the curve. Note that (1) is the barycentric equation of K010 which is the dual of H3. See also K244. 

on H3 : X(1553), X(6070), X(6071), X(6072), X(6073), X(6074), X(6075), X(6076), X(6077), X(14499) up to X(14507), vertices of the cevian triangle of X(69) on aH3 : X(14480), X(14508) up to X(14515), vertices of the circumtangential triangle 

The Steiner deltoid H3 (envelope of Simson lines) and its anticomplement aH3 (envelope of axis of inscribed parabolas) are two very famous curves in triangle geometry. There's no question of reconsidering here their very numerous properties. We will only point out their connection with some cubics or other curves. 


