Star polygon

[2] Star polygon names combine a numeral prefix, such as penta-, with the Greek suffix -gram (in this case generating the word pentagram).

A regular star polygon is denoted by its Schläfli symbol {p/q}, where p (the number of vertices) and q (the density) are relatively prime (they share no factors) and where q ≥ 2.

Regular star polygons were first studied systematically by Thomas Bradwardine, and later Johannes Kepler.

However, the vertices will be reached in the opposite direction, which makes a difference when retrograde polygons are incorporated in higher-dimensional polytopes.

Constructions based on stellation also allow regular polygonal compounds to be obtained in cases where the density q and amount p of vertices are not coprime.

Branko Grünbaum, in Tilings and patterns, represents such a star that matches the outline of a regular polygram {n/d} as |n/d|, or more generally with {n𝛼}, which denotes an isotoxal concave or convex simple 2n-gon with outer internal angle 𝛼.

Branko Grünbaum and Geoffrey Shephard consider two of them, as regular star n-gons and as isotoxal concave simple 2n-gons.

These three treatments are: When the area of the polygon is calculated, each of these approaches yields a different result.