Editing Star polygon (section)

==Interiors==
The interior of a star polygon may be treated in different ways. Three such treatments are illustrated for a pentagram. [[Branko Grünbaum]] and Geoffrey Shephard consider two of them, as regular star ''n''-gons and as isotoxal concave simple '''2'''''n''-gons.<ref name="maa.org"/>

[[File:Pentagram interpretations.svg|400px]]

These three treatments are:
* Where a line segment occurs, one side is treated as outside and the other as inside. This is shown in the left hand illustration and commonly occurs in computer [[vector graphics]] rendering.
* The number of times that the polygonal curve winds around a given region determines its ''[[Density (polytope)|density]]''. The exterior is given a density of 0, and any region of density > 0 is treated as internal. This is shown in the central illustration and commonly occurs in the mathematical treatment of [[polyhedra]]. (However, for non-orientable polyhedra, density can only be considered modulo 2 and hence, in those cases, for consistency, the first treatment is sometimes used instead.)
* Wherever a line segment may be drawn between two sides, the region in which the line segment lies is treated as inside the figure.<!--This definition of the interior is false for a concave figure, isn't it? Perhaps mentioning the outline of a polygram would help?--> This is shown in the right hand illustration and commonly occurs when making a physical model.

When the area of the polygon is calculated, each of these approaches yields a different result.