# RegularPolygon

gives the regular polygon with n vertices equally spaced around the unit circle.

RegularPolygon[r,n]

gives the regular polygon of radius r.

RegularPolygon[{r,θ},n]

starts at angle θ with respect to the axis.

RegularPolygon[{x,y},rspec,n]

centers the polygon at {x,y}.

# Details # Examples

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## Basic Examples(3)

A pentagon:

Different styles applied to RegularPolygon:

Area and centroid:

## Scope(17)

### Graphics(7)

#### Specification(4)

Generate an equilateral triangle, square, pentagon, hexagon, etc.:

Generate pentagons of varying radii:

Generate triangles of varying starting angles:

Place six hexagons equally spaced around the unit circle:

#### Styling(2)

Color directives specify the face colors of regular polygons:

FaceForm and EdgeForm can be used to specify the styles of the interior and boundary:

#### Coordinate(1)

Use Dynamic coordinates:

### Regions(10)

Embedding dimension:

Geometric dimension:

Point membership test:

Get conditions for point membership:

Area:

Centroid:

Distance from a point:

The distance to the nearest point in the unit disk:

Signed distance from a point:

Signed distance to the unit disk:

Nearest point in the region:

Nearest points:

A regular polygon is bounded:

Get its range:

Integrate over a hexagon:

Optimize over a hexagon:

Solve equations in a hexagon:

## Applications(4)

Create a star region by taking the RegionUnion of rotated triangles about a common origin:

Create 3D extrusions with RegionProduct:

Plot a function over a hexagon:

Some lattices will have regular polygons as their cells. Consider the lattice basis:

Generate lattice points and tiles:

Visualize the tiling and lattice points:

## Properties & Relations(3)

A RegularPolygon is a Polygon whose vertices are equally spaced around the unit circle:

Use CirclePoints to generate points equally spaced around the unit circle:

The area of a regular polygon on the unit circle as is the area of a unit Disk:

## Neat Examples(2)

A collection of random regular polygons:

Overlap regular polygons of increasing radii and vertices: