Equilateral polygon Equilateral polygon In geometry, three or more than three straight lines (or segment of a line) make a polygon and an equilateral polygon is a polygon which has all sides of the same length. Except in the triangle case, it need not be equiangular (need not have all angles equal), but if it does then it is a regular polygon. If the number of sides is at least five, an equilateral polygon need not be a convex polygon: it could be concave or even self-intersecting. All regular polygons and isotoxal polygons are equilateral. An equilateral triangle is a regular triangle
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