Star polygons in art and culture

Star polygons and polygonal compounds are the basis for numerous figures of significance in arts and culture. The figure may be the border or interior of the polygon, or one or more closed polygonal paths that include all of the border and also have some legs crossing the interior. The name is derived from the polygon's similarity to the diffraction spikes of astronomical stars, but specific uses may exploit the connection or not. Stars often represent the unity of states within a country when they are used as a part of the flag.

Emblematic use

 * In heraldry, a mullet is a star with straight arms and typically five points. A star with wavy rather than straight rays is called an estoile. The mullet, used as an heraldic charge, is the ensign of knightly rank, and every order of knighthood incorporates this symbol in some way. It has traditionally been used in British heraldry as a mark of cadency for the third son.
 * In Christian art, St. Bruno bears a star on his breast; Saint Dominic, Saint Humbert and Saint Peter of Alcantara have a star on their head or forehead.
 * The star with six (or less commonly five, sometimes seven) points is associated with law enforcement in the United States, and forms the basis of the sheriff's badge.

Three-pointed stars
The three-pointed star is used much less often than other types of stars. but it appears in one of the versions of the flag of the International Brigades in the Spanish civil war. It also appears in the symbol of the Mercedes-Benz car manufacturer.

Four-pointed stars
Several varieties of four-pointed stars were used in cultures around the world:

The 1914-15 star campaign medal of the British army was based on a four-pointed star. A compass rose in the form of a four pointed-star also appears in the flag of NATO and the flag of the country of Aruba. The seal of the (now cancelled) United States Civil Service Commission included a four-pointed star between the years 1963-1979. Four-pointed stars also appears in the symbols of the Subaru car company and Philips corporation.

Five-pointed stars
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. 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 golden five-pointed star is a very common ideogram in the western world, and has particularly strong associations with military power and war. Many communist countries (such as China and Vietnam) and symbols (the hammer and sickle) also incorporate five-pointed stars.

Six-pointed stars
Several varieties of six-pointed stars are used in cultures around the world:
 * If the collinear edges of a regular six-pointed star are connected, so that two interlaced triangles are formed, a symbol results that is variously known as the hexagram, Star of David, or Shield of David (Magen David). This symbol is most commonly associated with Judaism. It is also used in Christianity, Islam and Hinduism, but less frequently.
 * The Ahmadiyya flag, Lawa-e-Ahmaddiyat, contains a six-pointed star, adjacent to a crescent.
 * The Star of Life, which is a six-armed cross.
 * The municipal flag of Chicago has four six-pointed stars.
 * German and German-American hex signs and barn stars often incorporate both five- and six-pointed stars as central themes.
 * The six-pointed star is used as the symbol for the Folk Nation alliance of gangs from Chicago. Crip gang members tend to use this symbol also.

Apart from these, six-pointed star formations are rare as an ideograph in Western cultures except in the case of law enforcement badges. In astrology, some formations of a six-pointed star can signify fixed stars. In some rare instances, it can signify the date of birth on a gravestone, synonymous with the five-point star.

Political
A seven-pointed star appears in the flag and heraldic symbolism of Australia. In the Australian context, the seven points (also known as the Commonwealth Star, the Federation Star, the Seven Point Star, or the Star of Federation) is a seven-pointed star symbolising the Federation of Australia which came into force on 1 January 1901. Six points of the Star represent the six original states of the Commonwealth of Australia, while the seventh point represents the territories.

The seven-pointed stars stand in contrast to the vexillologically more conventional five-pointed stars.

The Seal of the Cherokee Nation has an acute gold seven-pointed star in its seal.

The seven-pointed star is also used as a symbol of the Trinitarios gang from New York City.

Heptagram
A heptagram or septagram is a seven-pointed star drawn with seven straight strokes. There are two kinds of heptagrams:
 * Acute heptagram, the {7/3} star polygon.
 * Obtuse heptagram, the {7/2} star polygon.

Other
The eight-pointed star is widely used in the Arabic states in decorative art,. It is sometimes similar star to the Star of Lakshmi formed from overlapping squares but may also appear in the form of the Rub el Hizb which adds a central circle to the design.

Nine-pointed stars
A nine-pointed star is the most common symbol of the Baháʼí Faith, the number nine being significant in the religion.

Eleven-pointed stars
The flag of the Federation of Malaya used the eleven-pointed star from 1950 until 1963, with the star representing the 11 member states of the federation.

Twelve-pointed stars
The flag of Nauru uses a twelve-pointed star representing the 12 tribes on the island.

Fourteen-pointed stars
In the Church of Nativity in Bethlehem the traditionally location of the birth of Jesus is marked by a silver star with 14 points that represents the three sets of 14 generations in the genealogy of Jesus. The flag of Malaysia uses the Federal Star, a fourteen-pointed star representing the unity between the 13 member states and the federal government.