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Star polygons feature prominently in art and culture. Such polygons may or may not be regular, but they are always highly symmetrical. Examples include: The {5/2} star pentagon is also known as a pentalpha or pentangle, and historically has been considered by many magical and religious cults to have occult significance.
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.
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 pentagram contains ten points (the five points of the star, and the five vertices of the inner pentagon) and fifteen line segments. It is represented by the Schläfli symbol {5/2}. Like a regular pentagon, and a regular pentagon with a pentagram constructed inside it, the regular pentagram has as its symmetry group the dihedral group of ...
The five points of a regular pentagram are golden triangles, [47] as are the ten triangles formed by connecting the vertices of a regular decagon to its center point. [48] Bisecting one of the base angles of the golden triangle subdivides it into a smaller golden triangle and a golden gnomon.
There is also a star figure, {9/3} or 3{3}, made from the regular enneagon points but connected as a compound of three equilateral triangles. [3] [4] (If the triangles are alternately interlaced, this results in a Brunnian link.) This star figure is sometimes known as the star of Goliath, after {6/2} or 2{3}, the star of David. [5]
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Star position is the apparent angular position of any given star in the sky, which seems fixed onto an arbitrary sphere centered on Earth. The location is defined by a pair of angular coordinates relative to the celestial equator: right ascension (α) and declination (δ). This pair based the equatorial coordinate system.