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Suppose that P does not lie on any of the extended sides BC, CA, AB, and let P −1 denote the isogonal conjugate of P. The pedal triangle of P is homothetic to the antipedal triangle of P −1 . The homothetic center (which is a triangle center if and only if P is a triangle center) is the point given in trilinear coordinates by
Isogonal conjugate transformation over the points inside the triangle. In geometry, the isogonal conjugate of a point P with respect to a triangle ABC is constructed by reflecting the lines PA, PB, PC about the angle bisectors of A, B, C respectively. These three reflected lines concur at the isogonal conjugate of P.
Isogonal figure. In geometry, a polytope (a polygon, polyhedron or tiling, for example) is isogonal or vertex-transitive if all its vertices are equivalent under the symmetries of the figure. This implies that each vertex is surrounded by the same kinds of face in the same or reverse order, and with the same angles between corresponding faces.
3 dimensions: políedres isogonals. Es poden classificar els políedres isogonals: Regulars si també són isoèdrics (cara-transitius) i isotoxals (costat-transitius). Això implca que cada cara és el mateix tipus de polígon regular. Quasi-regulars si també són isotoxals (costat-transitius) però no isoèdrics (cara-transitius).
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18 de ago. de 2017 · The Wikipedia page "Isotoxal Figure" said that an edge-transitive polyhedron or tiling must be vertex-transitive or face-transitive. I deleted that because it is false in general, as in the following example. Under what further conditions is it true, and how is it proven?
2 de abr. de 2023 · Isogonal mapping. A (differentiable) mapping that preserves angles. For instance, the stereographic projection of cartography has this property . See also Conformal mapping; Anti-conformal mapping. Isogonal circles. A circle is said to be isogonal with respect to two other circles if it makes the same angle with these two, . Isogonal line.
