Editing Stellation (section)

== Stellating polygons ==
[[File:regular star polygons.svg|thumb|upright=1.5|Regular convex and star polygons with 3 to 12 vertices labelled with their Schläfli symbols]]
Stellating a regular polygon symmetrically creates a regular [[star polygon]] or [[Star polygon#Star figures|polygonal compound]]. These polygons are characterised by the number of times ''m'' that the polygonal boundary winds around the centre of the figure. Like all regular polygons, their vertices lie on a circle. ''m'' also corresponds to the number of vertices around the circle to get from one end of a given edge to the other, starting at 1.

A regular star polygon is represented by its [[Schläfli symbol]] {''n''/''m''}, where ''n'' is the number of vertices, ''m'' is the ''step'' used in sequencing the edges around it, and ''m'' and ''n'' are [[coprime]] (have no common [[divisor|factor]]). The case ''m'' = 1 gives the convex polygon {''n''}. ''m'' also must be less than half of ''n''; otherwise the lines will either be parallel or diverge, preventing the figure from ever closing.<!--is there a term given to the figures which result when the lines are curved to meet?-->

If ''n'' and ''m'' do have a common factor, then the figure is a regular compound. For example {6/2} is the regular compound of two triangles {3} or [[hexagram]], while {10/4} is a compound of two pentagrams {5/2}. 

Some authors use the Schläfli symbol for such regular compounds. Others regard the symbol as indicating a single path which is wound ''m'' times around {{sfrac|''n''|''m''}} vertex points, such that one edge is superimposed upon another and each vertex point is visited ''m'' times. In this case a modified symbol may be used for the compound, for example 2{3} for the hexagram and 2{5/2} for the regular compound of two pentagrams.

A regular ''n''-gon has {{Sfrac|''n'' – 4|2}} stellations if ''n'' is [[parity (mathematics)|even]] (assuming compounds of multiple degenerate [[digon]]s are not considered), and {{Sfrac|''n'' – 3|2}} stellations if ''n'' is [[parity (mathematics)|odd]].
{{-}}
{| width=640 class="wikitable"
|[[Image:Pentagram green.svg|150px]]<BR>The [[pentagram]], {5/2}, is the only stellation of a [[pentagon]].
|[[File:Regular star figure 2(3,1).svg|150px]]<BR>The [[hexagram]], {6/2}, the stellation of a [[hexagon]] and a compound of two triangles
| rowspan=2 |[[Image:Enneagon stellations.svg|320px]]<BR>The [[enneagon]] (nonagon) {9} has 3 [[Enneagram (geometry)|enneagrammic]] forms:<BR>{9/2}, {9/3}, {9/4}, with {9/3} being a compound of 3 triangles.
|-
|colspan=2|[[Image:Obtuse heptagram.svg|150px]][[Image:Acute heptagram.svg|150px]]
<BR>The [[heptagon]] has two [[heptagram]]mic forms:<BR>{7/2}, {7/3}
|}

Like the [[heptagon]], the [[octagon]] also has two [[octagram]]mic stellations, one, {8/3} being a [[star polygon]], and the other, {8/2}, being the compound of two [[Square (geometry)|squares]].