A convex pentagon

In geometry, a convex polygon is a simple polygon whose interior is a convex set. The following properties of a simple polygon are all equivalent to convexity: Image File history File links Pentagon. ... Image File history File links Pentagon. ... Table of Geometry, from the 1728 Cyclopaedia. ... A simple concave hexagon In geometry, two edges of a polygon may cross or even overlap in general. ... Look up Convex set in Wiktionary, the free dictionary. ...

• Every internal angle is at most 180 degrees.
• Every line segment between two vertices of the polygon does not go exterior to the polygon (i.e., it remains inside or on the boundary of the polygon).

A simple polygon is strictly convex if every internal angle is strictly less than 180 degrees. Equivalently, a polygon is strictly convex if every line segment between two vertices of the polygon is strictly interior to the polygon except at its endpoints. In geometry, an internal angle is an angle that 2 sides of a polygon form by touching. ... A degree (in full, a degree of arc, arc degree, or arcdegree), usually symbolized °, is a measurement of plane angle, representing 1／360 of a full rotation. ... The geometric definition of a line segment In geometry, a line segment is a part of a line that is bounded by two end points, and contains every point on the line between its end points. ... In geometry, a vertex (Latin: whirl, whirlpool; plural vertices) is a corner of a polygon (where two sides meet) or of a polyhedron (where three or more faces and an equal number of edges meet). ...

Every triangle is strictly convex. A triangle is one of the basic shapes of geometry: a polygon with three vertices and three sides which are straight line segments. ...

Concave polygon

A simple concave hexagon

If a simple polygon is not convex, it is called concave. At least one internal angle of a concave polygon is larger than 180 degrees. A simple polygon, created with GIMP, in the public domain. ... A simple polygon, created with GIMP, in the public domain. ... In geometry, an internal angle is an angle that 2 sides of a polygon form by touching. ...

A concave polygon is often called re-entrant polygon (but in some cases the latter term has a different meaning). A re-entrant, or concave polygon is one in which at least one interior angle is more than 180 degrees (i. ...

External links

• Definition and properties of convex polygons With interactive animation
• Definition and properties of concave polygons With interactive animation