Corners

Corners are the points at which two edges of a geometric figure meet. In two-dimensional shapes, a corner is the vertex where two sides of a polygon meet, and the angle inside the shape at that vertex is called the interior angle. In three-dimensional objects, corners occur where two or more faces intersect, forming a vertex with a dihedral angle between the adjacent faces.

For polygons, corners are classified as convex when the interior angle is less than 180 degrees and concave when it is greater than 180 degrees. Some shapes may have both convex and concave corners. The sum of interior angles of a simple polygon with n sides is (n−2)×180 degrees; this restricts the possible sets of corner angles.

In physical design and manufacturing, the term corner also refers to the sharpness of a corner. Sharp corners can be weakened or rounded through fillets (rounded transitions) or chamfers (beveled edges) to improve strength, safety, or aesthetics. Architectural and carpentry practices often modify interior and exterior corners to ensure proper fit and weather sealing.

Common examples include a square, with four 90-degree corners; a triangle, with three corners whose interior angles sum to 180 degrees; and a cube, which has eight corners. In math and computer graphics, corners are used as key points in meshes and shapes, often treated as vertices for rendering and geometric computations.