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In geometry, a star polygon is a type of non-convex polygon. Regular star polygons have been studied in depth; while star polygons in general appear not to have been formally defined, certain notable ones can arise through truncation operations on regular simple or star polygons.
The regular octagonal star is very popular as a symbol of rowing clubs in the Cologne Lowland, as seen on the club flag of the Cologne Rowing Association. The geometry can be adjusted so 3 edges cross at a single point, like the Auseklis symbol An 8-point compass rose can be seen as an octagonal star, with 4 primary points, and 4 secondary points.
Koch snowflakes drawn with MSWLogo (in Tartapelago [41]) Drawing of a pentagram with notations of its angles. The pentagram is the simplest regular star polygon. 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}.
The heptagram is known among neopagans as the Elven Star or Fairy Star. It is treated as a sacred symbol in various modern pagan and witchcraft traditions. Blue Star Wicca also uses the symbol, where it is referred to as a septegram. The second heptagram is a symbol of magical power in some pagan spiritualities.
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.
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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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]