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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.
An isogon may refer to: Isogonal figure - a polygon or polyhedron with all of its vertices equivalent under the symmetries of the figure.
Isogonal, a mathematical term meaning "having similar angles", may refer to: Isogonal figure or polygon, polyhedron, polytope or tiling; Isogonal trajectory, in curve theory; Isogonal conjugate, in triangle geometry
Individual polygons are named (and sometimes classified) according to the number of sides, combining a Greek-derived numerical prefix with the suffix -gon, e.g. pentagon, dodecagon. The triangle , quadrilateral and nonagon are exceptions, although the regular forms trigon , tetragon , and enneagon are sometimes encountered as well.
A simple polygon is the boundary of a region of the plane that is called a solid polygon. The interior of a solid polygon is its body, also known as a polygonal region or polygonal area. In contexts where one is concerned only with simple and solid polygons, a polygon may refer only to a simple polygon or to a solid polygon.
The rule of Vs: sharp-pointed vees usually are in stream valleys, with the drainage channel passing through the point of the vee, with the vee pointing upstream. This is a consequence of erosion . The rule of Os : closed loops are normally uphill on the inside and downhill on the outside, and the innermost loop is the highest area.
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. An indirect equiangular polygon can include angles turning right or left in any combination. A skew equiangular polygon may be isogonal, but can't be considered direct since it is ...
Simple polygons are sometimes called Jordan polygons, because they are Jordan curves; the Jordan curve theorem can be used to prove that such a polygon divides the plane into two regions. [8] Indeed, Camille Jordan's original proof of this theorem took the special case of simple polygons (stated without proof) as its starting point. [9]