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Regular polygons may be either convex or star. In the limit, a sequence of regular polygons with an increasing number of sides approximates a circle, if the perimeter or area is fixed, or a regular apeirogon (effectively a straight line), if the edge length is fixed.
An example of a convex polygon: a regular pentagon.. In geometry, a convex polygon is a polygon that is the boundary of a convex set.This means that the line segment between two points of the polygon is contained in the union of the interior and the boundary of the polygon.
There are 17 combinations of regular convex polygons that form 21 types of plane-vertex tilings. [6] [7] Polygons in these meet at a point with no gap or overlap. Listing by their vertex figures, one has 6 polygons, three have 5 polygons, seven have 4 polygons, and ten have 3 polygons. [8]
The area of a regular hexagon ... In any convex equilateral hexagon (one with all sides equal) with common side a, there exists [11]: p.184, #286.3 ...
Sum S of internal angles of a regular convex polygon with n sides: = Area A of a regular convex polygon with n sides and side length s: = Inradius r of a regular convex polygon with n sides and side length s:
Polygons have been known since ancient times. The regular polygons were known to the ancient Greeks, with the pentagram, a non-convex regular polygon (star polygon), appearing as early as the 7th century B.C. on a krater by Aristophanes, found at Caere and now in the Capitoline Museum. [40] [41]
The polytopes of rank 2 (2-polytopes) are called polygons. Regular polygons are equilateral and cyclic. A p-gonal regular polygon is represented by Schläfli symbol {p}. Many sources only consider convex polygons, but star polygons, like the pentagram, when considered, can also be regular. They use the same vertices as the convex forms, but ...
Uniform polyhedra are vertex-transitive and every face is a regular polygon. They may be subdivided into the regular, quasi-regular, or semi-regular, and may be convex or starry. The duals of the uniform polyhedra have irregular faces but are face-transitive, and every vertex figure is a regular polygon. A uniform polyhedron has the same ...