About the Geometry of a Five-Point Star

About the Geometry of a Five-Point Star
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A five pointed star is a common symbol on flags and in religion. A golden five pointed star, is a star that has points of equal length and equal angles of 36 degrees at each point.


A five pointed star is a common ideogram in many concepts throughout the world, and is featured on many flags and in religious symbols as well.


When a five pointed star is drawn using points of equal length along with 36 degree angles at each point, then the five pointed star is often referred to as a golden five pointed star. The pentagram is the simplest regular star polygon, containing ten points. Five points make up the tips of the star, and five points make up the vertices of the inner pentagon. The pentagram or five point star also consists of fifteen different line segments. By joining the collinear edges of the five point star together, a pentagon is produced. Like a regular pentagon, and like a regular pentagon that has a pentagram constructed within it, the regular pentagram has the dihedral group of order 10 as its symmetry group.


Not only does a standard five point star have a pentagon in its middle, but when you connect the five points together with line segments, you will have created a proportional pentagon on its outer edges as well. Additionally, you can form a golden five point star using a series of embedded pentagrams.


While not all five pointed stars have to possess points of the same length and points of equal angles, golden five pointed stars are perfect in this regard. A regular polygon, like the one that sits in the center of a five pointed star, has equal angles of 108 degrees each. The points of a golden five pointed star are all 36 degrees each, making the other two angles of each point of the star 72 degrees each. Five pointed stars can have points with unique line segment lengths and different angled points, but these are not golden five pointed stars, meaning that their points are not equal to one another.


The only characteristic that makes a five pointed star what it is, is possessing five points constructed from connecting line segments. The rules relating to golden five pointed stars are much more specific, however, dictating specific angles and equal lengths of each of the five points.

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