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In Euclidean geometry, an equiangular polygon is a polygon whose vertex angles are equal. If the lengths of the sides are also equal (that is, if it is also equilateral) then it is a regular polygon. Isogonal polygons are equiangular polygons which alternate two edge lengths. For clarity, a planar equiangular polygon can be called direct or ...
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.
Computing the maximum number of equiangular lines in n-dimensional Euclidean space is a difficult problem, and unsolved in general, though bounds are known. The maximal number of equiangular lines in 2-dimensional Euclidean space is 3: we can take the lines through opposite vertices of a regular hexagon, each at an angle 120 degrees from the other two.
An isogon (from Ancient Greek γωνία (gonia) 'angle') is a contour line for a variable which measures direction. In meteorology and in geomagnetics, the term isogon has specific meanings which are described below.
An isogon may refer to: Isogonal figure - a polygon or polyhedron with all of its vertices equivalent under the symmetries of the figure. A type of contour line Contour line#Types
Grünbaum and Shephard call these tilings uniform although it contradicts Coxeter's definition for uniformity which requires edge-to-edge regular polygons. [17] Such isogonal tilings are actually topologically identical to the uniform tilings, with different geometric proportions.
In Euclidean geometry, a regular polygon is a polygon that is direct equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may be either convex or star.
Equiangular may refer to: . Equiangular lines, a set of lines where every pair of lines makes the same angle; Equiangular polygon, a polygon with equal angles; Logarithmic spiral or equiangular spiral, a type of geometric spiral
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