Regular polygon is denoted by its Schläfli symbol {"n"}. For "n" < 3, we have two degenerate cases: In certain contexts all the polygons considered will be regular. In such circumstances it is customary to drop the prefix regular. For instance, all the faces of uniform polyhedra must be regular and the faces will be described simply as triangle, square, pentagon, etc. For a regular convex "n"-gon, each interior angle has a measure of: and each exterior angle (i.e., supplementary to the interior angle) has a measure of formula_5 degrees, with the sum of the exterior angles equal to 360 degrees or
Regular polygon "n"-gon, the sum of the perpendicular distances from any interior point to the "n" sides is "n" times the apothem (the apothem being the distance from the center to any side). This is a generalization of Viviani's theorem for the "n"=3 case. The circumradius "R" from the center of a regular polygon to one of the vertices is related to the side length "s" or to the apothem "a" by For constructible polygons, algebraic expressions for these relationships exist; see Bicentric polygon#Regular polygons. The sum of the perpendiculars from a regular "n"-gon's vertices to any line tangent to the circumcircle