Stars
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A regular n-pointed star, n≥3, is a non-convex polygon that has:
a) 2n sides of equal length,
b) Two sets of n vertices that alternate on two concentric circles. The n vertices of the same type are separated by arcs of angle α = 360º/n and adjacent vertices of different type are separated by arcs of angle α/2 = 180º/n.
The center of the regular star is the center O of the concentric circles. All exterior vertices have interior angle β < 180º - α and all interior vertices have exterior angle ϒ = α + β.
Examples of 8-pointed regular stars
Ornamentation of a star
Ornamentation of a star
It is customary to decorate the empty space in the central part of a regular star generating a new n-pointed central star surrounded by n quadrilaterals shaped like a kite.
a) Regular star with 2 layers; b) kite and central star
Examples of 12-pointed and 16-pointed regular stars with 2 layers
Coloring of a star
Coloring of a star
The same star can have different aesthetic qualities depending on whether it is represented by lines or in the form of a mosaic coloring the different layers.
9-pointed regular star with 2 layers: a) without coloring; b) colored
10-pointed regular star with 2 layers: a) without coloring; b) colored
Ornamentation of the exterior of a regular star
The exterior of a regular star with 2 layers may also be adorned, for example, with a ring of squares, pentagons, or hexagons.
Regular stars with two layers with: a) squares; b) pentagons; c) hexagons
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