# Polygon

Polygon[{p1,,pn}]

represents a filled polygon with points pi.

Polygon[{p1,,pn}{{q1,,qm},}]

represents a polygon with holes {q1,,qm},.

Polygon[{poly1,poly2,}]

represents a collection of polygons polyi.

Polygon[{p1,,pn},data]

represents a polygon in which coordinates given as integers i in data are taken to be pi.

# Details and Options

• Polygon can be used as a geometric region and a graphics primitive.
• Polygon[{p1,,pn}] is a plane region, representing all the points inside the closed curve with line segments {p1,p2},,{pn-1,pn} and {pn,p1}.
• A point is an element of the polygon if a ray from the point in any direction in the plane crosses the boundary line segments an odd number of times.
• Polygon[{p1,,pn}{{q1,,qm},}] specifies a polygon with holes consisting of an outer polygon Polygon[{p1,,pn}] and one or several inner polygons Polygon[{q1,,qm}],.
• A point is an element of the polygon if it is in the outer polygon but not in any inner polygon.
• Polygon[{poly1,poly2,}] is a collection of polygons polyi with or without holes and is treated as a union of polyi for geometric computations.
• Polygon[{p1,,pn},data] effectively replaces integers i that appear as coordinates in data by the corresponding pi.
•  Polygon[{p1,…,pn},{b1,…,bn}] polygon boundary points {pb1,…,pbk} Polygon[{p1,…,pn},{{o1,…,ok}{{i1,…,il},…}] outer polygon boundary points {po1,…,pok} and inner polygon boundary {pi1,…,pil} etc. Polygon[{p1,…,pn},{{b1,…,bn},{o1,…,ok}{{i1,…,il},…},…}] a collection of several polygons
• As a geometric region, the points pi can have any embedding dimension, but must all lie in a plane and have the same embedding dimension.
• In a graphic, the points pi can be Scaled, Offset, ImageScaled and Dynamic expressions.
• Graphics rendering is affected by directives such as FaceForm, EdgeForm, Texture, Specularity, Opacity and color.
• FaceForm[front,back] can be used to specify different styles for the front and back of polygons in 3D. The front is defined by the right-hand rule and the direction of the first three points.
• The following options and settings can be used in graphics:
•  VertexColors Automatic vertex colors to be interpolated VertexNormals Automatic effective vertex normals for shading VertexTextureCoordinates None coordinates for textures
• Point can be used with symbolic points in GeometricScene.

# Examples

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## Basic Examples(2)

A polygon:

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Its graphic image:

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Its area:

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Differently styled 3D polygons:

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## Neat Examples(3)

Introduced in 1988
(1.0)
|
Updated in 2019
(12.0)