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Isogonal figure. In geometry, a polytope (e.g. a polygon or polyhedron) or a tiling 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.
Isogonal polygons are equiangular polygons which alternate two edge lengths. For clarity, a planar equiangular polygon can be called direct or indirect. A direct equiangular polygon has all angles turning in the same direction in a plane and can include multiple turns. Convex equiangular polygons are always direct.
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Apr 2, 2023 · Literally "same angle" . There are several concepts in mathematics involving isogonality. Contents. 1 Isogonal trajectory. 2 Isogonal mapping. 3 Isogonal circles. 4 Isogonal line. 4.1 References. Isogonal trajectory. A trajectory that meets a given family of curves at a constant angle. See Isogonal trajectory . Isogonal mapping.
Isogonal figure explained. In geometry, a polytope (e.g. a polygon or polyhedron) or a tiling 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 ...
Proof. Point is the isogonal conjugate of a point with respect to a triangle so point is the isogonal conjugate of a point with respect to a triangle. Points and lies on the same line, therefore. Point lies on circles and spiral similarity centered at transform triangle to. vladimir.shelomovskii@gmail.com, vvsss.
Aug 18, 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?
