A p-gon is regular if it is both equilateral and equiangular.

A regular polygon is easily seen to have a center, from which all the vertices are at the same distance R0, while all the sides are at the same distance R1. This means that there are two concentric circles, the circum-circle and the in-circle, which pass through the vertices and touch the sides, respectively.

To access the information relating to a regular polygon p, use the following function calls:

The command with(geometry,RegularPolygon) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{geometry}\right)\:$

$\mathrm{RegularPolygon}\left(\mathrm{gon}\,5\,\mathrm{point}\left(o\,1\,1\right)\,2\right)$

$\mathrm{gon}$

$\mathrm{detail}\left(\mathrm{gon}\right)$

$\begin{array}{ll}\text{name of the object}& \mathrm{gon}\\ \text{form of the object}& \mathrm{RegularPolygon2d}\\ \text{the side of the polygon}& 4\sin \left(\frac{\mathrm{\pi }}{5}\right)\\ \text{the center of the polygon}& \left[1\,1\right]\\ \text{the radius of the circum-circle}& 2\\ \text{the radius of the in-circle}& 2\cos \left(\frac{\mathrm{\pi }}{5}\right)\\ \text{the interior angle}& \frac{3\mathrm{\pi }}{5}\\ \text{the exterior angle}& \frac{2\mathrm{\pi }}{5}\\ \text{the perimeter}& 20\sin \left(\frac{\mathrm{\pi }}{5}\right)\\ \text{the area}& 20\sin \left(\frac{\mathrm{\pi }}{5}\right)\cos \left(\frac{\mathrm{\pi }}{5}\right)\\ \text{the vertices of the polygon}& \left[\left[3\,1\right]\,\left[1+2\cos \left(\frac{2\mathrm{\pi }}{5}\right)\,1+2\sin \left(\frac{2\mathrm{\pi }}{5}\right)\right]\,\left[1-2\cos \left(\frac{\mathrm{\pi }}{5}\right)\,1+2\sin \left(\frac{\mathrm{\pi }}{5}\right)\right]\,\left[1-2\cos \left(\frac{\mathrm{\pi }}{5}\right)\,1-2\sin \left(\frac{\mathrm{\pi }}{5}\right)\right]\,\left[1+2\cos \left(\frac{2\mathrm{\pi }}{5}\right)\,1-2\sin \left(\frac{2\mathrm{\pi }}{5}\right)\right]\right]\end{array}$