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A regular star pentagon, {5/2}, has five vertices (its corner tips) and five intersecting edges, while a concave decagon, |5/2|, has ten edges and two sets of five vertices. The first is used in definitions of star polyhedra and star uniform tilings , while the second is sometimes used in planar tilings.
In geometry, a pentagon (from Greek πέντε (pente) 'five' and γωνία (gonia) 'angle' [1]) is any five-sided polygon or 5-gon. The sum of the internal angles in a simple pentagon is 540°. A pentagon may be simple or self-intersecting. A self-intersecting regular pentagon (or star pentagon) is called a pentagram.
The five-pointed star is a symbol of the Baháʼí Faith. [28] [29] In the Baháʼí Faith, the star is known as the Haykal (Arabic: "temple"), and it was initiated and established by the Báb. The Báb and Bahá'u'lláh wrote various works in the form of a pentagram. [30] [31]
A five-pointed star. A five-pointed star (☆), geometrically an equilateral concave decagon, is a common ideogram in modern culture. Comparatively rare in classical heraldry, it was notably introduced for the flag of the United States in the Flag Act of 1777 and since has become widely used in flags.
The interior angle concept can be extended in a consistent way to crossed polygons such as star polygons by using the concept of directed angles.In general, the interior angle sum in degrees of any closed polygon, including crossed (self-intersecting) ones, is then given by 180(n–2k)°, where n is the number of vertices, and the strictly positive integer k is the number of total (360 ...
A shrinking argument also eliminates 5-fold symmetry. Consider a regular pentagon of lattice points. If it exists, then we can take every other edge displacement and (head-to-tail) assemble a 5-point star, with the last edge returning to the starting point. The vertices of such a star are again vertices of a regular pentagon with 5-fold ...
Five-pointed star. The five-pointed star, if drawn with points of equal length and angles of 36° at each point, is sometimes termed a golden five pointed star. [7] If the colinear edges are joined, a pentagram is produced, which is the simplest of the unicursal star polygons, and a symbol of mystical and magical significance.
The sum of any icositetragon's interior angles is 3960 degrees. ... There are also 7 regular star figures using the same vertex arrangement: 2{12}, 3{8}, 4{6 ...