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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.
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 ...
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.
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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.
An n-pointed magic star is a star polygon with Schläfli symbol {n/2} [1] in which numbers are placed at each of the n vertices and n intersections, such that the four numbers on each line sum to the same magic constant. [2] A normal magic star contains the integers from 1 to 2n with no numbers repeated. [3]
Sample configurations of pentagramma mirificum Relations between the angles and sides of five right triangles adjacent to the inner pentagon. Their Napier’s circles contain circular shifts of parts ( a , {\displaystyle (a,} π / 2 − B , {\displaystyle \pi /2-B,} π / 2 − c , {\displaystyle \pi /2-c,} π / 2 − A , {\displaystyle \pi /2-A ...
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