Polygons are fundamental geometric shapes that are widely used in mathematics, computer graphics, and various fields of science and engineering. A polygon is a two-dimensional closed figure with straight sides or edges.

## Here are key points about polygons:

Definition: A polygon is defined as a flat, closed shape with straight sides. It is formed by connecting at least three non-collinear (not lying in a straight line) points called vertices.

Edges: The straight sides of a polygon are called edges. Each edge connects two adjacent vertices. The total number of edges in a polygon is equal to the number of sides.

Vertices: The points where the edges of a polygon meet are called vertices. The number of vertices is equal to the number of sides in a polygon.

Sides: The line segments that form the edges of a polygon are called sides. The length of each side can vary, but all sides of a polygon must be straight.

Interior: The region enclosed by the sides of a polygon is called the interior or the interior region of the polygon. It is also known as the polygon’s “area.”

Exterior: The space outside the sides of a polygon is called the exterior or the exterior region of the polygon.

Convex and Concave: Polygons are classified into two main categories based on their shape:

• Convex Polygon: All interior angles of a convex polygon are less than 180 degrees, and any line segment connecting two points within the interior of the polygon lies entirely inside the polygon.
• Concave Polygon: A concave polygon has at least one interior angle greater than 180 degrees, and it may contain “dents” or “cut-outs.”

Regular and Irregular: A regular polygon is one in which all sides are of equal length and all interior angles are equal. Irregular polygons have sides and angles of varying lengths and measures.

Types: Common examples of polygons include triangles (3 sides), quadrilaterals (4 sides), pentagons (5 sides), hexagons (6 sides), heptagons (7 sides), octagons (8 sides), and more.

Polygons in Computer Graphics: Polygons are extensively used in computer graphics to create 2D and 3D shapes and objects. Triangles and quadrilaterals (often in the form of rectangles or squares) are particularly common for modeling complex surfaces.

Tessellation: The process of subdividing a surface into polygons, typically triangles or quadrilaterals, is called tessellation. This technique is used to represent curved surfaces with many small, flat polygons, making them suitable for computer graphics and rendering.

Applications: Polygons are used in various applications, including architectural design, computer-aided design (CAD), video game development, geographic information systems (GIS), and more.

Polygons are essential geometric shapes with diverse applications in mathematics, science, engineering, and computer graphics. They provide a versatile and flexible way to represent and model complex shapes and surfaces.