Editing Star polygon (section)

{{Short description|Regular non-convex polygon}}
{{Distinguish|Star-shaped polygon}}
{| class=wikitable align=right width=320 style="margin: 0px 0px 10px 10px"
|+ Two types of star pentagons
|- align=center
|[[File:Alfkors.svg|160px]]<BR>{5/2}
|[[File:Stjärna.svg|160px]]<BR>{{pipe}}5/2{{pipe}}
|-
|colspan=2|A regular star [[pentagon]], {5/2}, has five vertices (its corner tips) and five intersecting edges, while a concave [[decagon]], {{pipe}}5/2{{pipe}}, has ten edges and two sets of five vertices. The first is used in definitions of [[star polyhedra]] and star [[uniform tiling]]s, while the second is sometimes used in planar tilings.
|- align=center
|[[File:Small stellated dodecahedron.png|160px]]<BR>[[Small stellated dodecahedron]]
|[[File:Kepler decagon pentagon pentagram tiling.svg|160px]]<BR>[[Tessellation]]
|}

In [[geometry]], a '''star polygon''' is a type of non-[[convex polygon]]. '''Regular star polygons''' have been studied in depth; while star polygons in general appear not to have been formally defined, [[Decagram (geometry)#Related figures|certain notable ones]] can arise through truncation operations on regular simple or star polygons.

[[Branko Grünbaum]] identified two primary usages of this terminology by [[Johannes Kepler]], one corresponding to the [[regular star polygon]]s with [[List of self-intersecting polygons|intersecting edges]] that do not generate new vertices, and the other one to the [[isotoxal]] [[Concave polygon|concave]] [[simple polygon]]s.<ref name=tilingsandpatterns>Grünbaum & Shephard (1987). Tilings and Patterns. Section 2.5</ref>

[[Polygram (geometry)|Polygrams]] include polygons like the [[pentagram]], but also compound figures like the [[hexagram]].

One definition of a ''star polygon'', used in [[turtle graphics]], is a polygon having ''q'' ≥ 2 [[Turn (geometry)|turns]] (''q'' is called the [[turning number]] or [[Density (polygon)|density]]), like in [[spirolateral]]s.<ref name="turtle">Abelson, Harold, diSessa, Andera, 1980, ''Turtle Geometry'', MIT Press, p. 24</ref>