define a regular polygon
RegularPolygon(p, n, cen, rad)
the name of the regular polygon
positive integer >= 3
point which is the center of the n-gon
number which is the radius of the circumscribed circle of the n-gon
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:
returns the form of the geometric object
(i.e., RegularPolygon2d if p is a regular polygon).
returns a list of vertices of p.
returns the side of p.
returns the center of p.
returns the radius of the circum-circle of p.
returns the radius of the in-circle of p.
returns the interior angle of p.
returns the exterior angle of p.
returns the apothem of p.
returns the perimeter of p.
returns the area of p.
returns a detailed description of the
given regular polygon p.
The command with(geometry,RegularPolygon) allows the use of the abbreviated form of this command.
name of the objectgonform of the objectRegularPolygon2dthe side of the polygon4⁢sin⁡π5the center of the polygon1,1the radius of the circum-circle2the radius of the in-circle2⁢cos⁡π5the interior angle3⁢π5the exterior angle2⁢π5the perimeter20⁢sin⁡π5the area20⁢sin⁡π5⁢cos⁡π5the vertices of the polygon3,1,1+2⁢cos⁡2⁢π5,1+2⁢sin⁡2⁢π5,1−2⁢cos⁡π5,1+2⁢sin⁡π5,1−2⁢cos⁡π5,1−2⁢sin⁡π5,1+2⁢cos⁡2⁢π5,1−2⁢sin⁡2⁢π5
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