How to Create Regular Star Polygons

Star Polygons

Star polygons are non-convex polygons that look like a star. They are created by connecting non-adjacent vertex of a polygon and continuing the process until the first vertex is reached again.

star polygons

Star polygons created from regular polygons are called regular star polygons. Four regular star polygons are shown above.

Creating Regular Star Polygons

Regular star polygons can be created by placing equally spaced points on a circle. For example, if you want to create a star polygon using a dodecagon (12-sided polygon) and connecting every fifth point, you can do the following:

1. Divide the central angle by the number of points (360/12 = 30 degrees).

2. Create a point on the circle.

3. Using the point create a central angle measuring 30 degrees.

4. Repeat Steps 2 and 3 to complete the 12 points.

star polygons

5. Connect every 5th point until the starting point is reached.

Now create other regular star polygons by changing the number of equally spaced points and the nth connection.

Naming Star Polygons 

Regular star polygons are named {p/q} where p is the number of equally spaced points on the circle connected every qth point. The blue star above for example is named {7/2} because there are 7 equally spaced points and the connection is done every 2nd point.  The names of the other stars above are {7/3}, {12/5} and {9/2}.

References: The Mathematical Palette,  Wolfram Math World

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