Given [math]p[/math] equally spaced points on a circle and a step [math]q\in\mathbb{N}[/math] a [i][color=#1e84cc]regular star polygon[/color][/i] [math]\{p/q\}[/math] is obtained by connecting each of the [math]p[/math] points to the point that is [math]q[/math] steps ahead in the cyclic ordering, when [math]p[/math] and [math]q[/math] are coprime.[br][br]The notation [math]\{p/q\}[/math] was introduced by the Swiss mathematician Ludwig Schläfli in the first half of the 19th century.[br][br]Regular polygons can be seen as the special case [math]\{p/1\}[/math] of regular star polygons. [br]

[u]Similarity Property[/u] [br]When [math]p[/math] and [math]q[/math] are coprime, hence a regular star polygon is generated, the intersection points of consecutive edges form a new regular [math]p[/math]-gon, that is similar to the initial regular [math]p[/math]-gon, and concentric with it.[br][br][u]Angles Measure Property[/u][br]When [math]p[/math] and [math]q[/math] are coprime, hence a regular star polygon is generated, each interior (vertex) angle measures [math]\theta=\pi-\frac{2\pi q}{p}[/math].[br][br]Interact with the app below to generate the inner [math]p[/math]-gons and view the measure of the interior angles.[br]