Editing Regular polygon (section)

{{short description|Equiangular and equilateral polygon}}
<div class="skin-invert-image">{{Infobox
| title    = Regular polygon
| above    = {{Image array
|width = 80
|perrow = 3
|image1 = Regular polygon 3 annotated.svg   |alt1 = Regular triangle
|image2 = Regular polygon 4 annotated.svg   |alt2 = Regular square
|image3 = Regular polygon 5 annotated.svg   |alt3 = Regular pentagon
|image4 = Regular polygon 6 annotated.svg   |alt4 = Regular hexagon
|image5 = Regular polygon 7 annotated.svg   |alt5 = Regular heptagon
|image6 = Regular polygon 8 annotated.svg   |alt6 = Regular octagon
|image7 = Regular polygon 9 annotated.svg   |alt7 = Regular nonagon
|image8 = Regular polygon 10 annotated.svg  |alt8 = Regular decagon
|image9 = Regular polygon 11 annotated.svg  |alt9 = Regular hendecagon
|image10 = Regular polygon 12 annotated.svg |alt10 = Regular dodecagon
|image11 = Regular polygon 13 annotated.svg |alt11 = Regular tridecagon
|image12 = Regular polygon 14 annotated.svg |alt12 = Regular tetradecagon
}}

| label1   = [[Edge (geometry)|Edge]]s and [[Vertex (geometry)|vertices]]
|  data1   = <math>n</math>

| label2   = [[Schläfli symbol]]
|  data2   = <math>\{n\}</math>

| label3   = [[Coxeter–Dynkin diagram]]
|  data3   = {{CDD|node_1|n|node}}

| label4   = [[Point group|Symmetry group]]
|  data4   = [[Dihedral symmetry|D<sub>n</sub>]], order 2n

| label5   = [[Dual polygon]]
|  data5   = Self-dual

| label6   = [[Area]]<br /> (with side length <math>s</math>)
|  data6   = <math>A = \tfrac{1}{4}ns^2 \cot\left(\frac{\pi}{n}\right)</math>

| label7   = [[Internal angle]]
|  data7   = <math>(n - 2) \times \frac{{\pi}}{n}</math>

| label8   = Internal angle sum
|  data8   = <math>\left(n - 2\right)\times {\pi}</math>

| label9   = Inscribed circle diameter
|  data9   = <math>d_\text{IC} = s\cot\left(\frac{\pi}{n}\right)</math>

| label10   = Circumscribed circle diameter
|  data10   = <math>d_\text{OC} = s\csc\left(\frac{\pi}{n}\right)</math>

| label11   = Properties
|  data11   = [[Convex polygon|Convex]], [[Cyclic polygon|cyclic]], [[Equilateral polygon|equilateral]], [[isogonal figure|isogonal]], [[isotoxal figure|isotoxal]]
}}</div>

In [[Euclidean geometry]], a '''regular polygon''' is a [[polygon]] that is [[Equiangular polygon|direct equiangular]] (all angles are equal in measure) and [[Equilateral polygon|equilateral]] (all sides have the same length). Regular polygons may be either ''[[convex polygon|convex]]'' or ''[[star polygon|star]]''. In the [[limit (mathematics)|limit]], a sequence of regular polygons with an increasing number of sides approximates a [[circle]], if the [[perimeter]] or [[area]] is fixed, or a regular [[apeirogon]] (effectively a [[Line (geometry)|straight line]]), if the edge length is fixed.