Geometrically an octagon is a polygon that has eight sides. 

A regular octagon is a closed figure with sides of the same length and internal angles of the same size. It has eight lines of reflective symmetry and rotational symmetry of order 8. The internal angle at each vertex of a regular octagon is 135°and the sum of all the internal angles of any octagon is 1080° (as with all polygons, the external angles total 360°).

The octagonal shape is used as a design element in architecture. The Dome of the Rock has a characteristic octagonal plan.

Umbrellas often have an octagonal outline.