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Three colored polygons are shown side by side: a red triangle, a yellow quadrilateral, and a green pentagon, each labeled above with its name. Figure 2: The points of a plane that are not on a polygon are separated by the polygon into two regions, the “inside” and the “outside.” Figure 1: A polygon whose vertices are lattice points. Platonic solids
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Italian-born physicist Dr. Enrico Fermi draws a diagram at a blackboard with mathematical equations. circa 1950.
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Carl Friedrich Gauss
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Three colored polygons are shown side by side: a red triangle, a yellow quadrilateral, and a green pentagon, each labeled above with its name.
Three types of polygons The three simplest polygons are the triangle, which has three sides; the quadrilateral, which has four sides; and the pentagon, which has five sides.

polygon

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polygon, in geometry, any closed curve consisting of a set of line segments (sides) connected such that no two segments cross. The simplest polygons are triangles (three sides), quadrilaterals (four sides), and pentagons (five sides).

If none of the sides, when extended, intersects the polygon, it is a convex polygon. Otherwise, it is concave.

A polygon with all sides equal is equilateral; an example is a rhombus, which is an equilateral quadrilateral. A polygon with all interior angles equal is equiangular; an example is a rectangle, which is an equiangular quadrilateral. Any polygon that is both equilateral and equiangular is a regular polygon; examples are an equilateral triangle and a square.

Italian-born physicist Dr. Enrico Fermi draws a diagram at a blackboard with mathematical equations. circa 1950.
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The Editors of Encyclopaedia BritannicaThis article was most recently revised and updated by J.E. Luebering.