the digon as a true polygon because of this.) 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. Angles For a regular convex n-gon, each interior angle has a measure of: degrees; radians; or full turns, and each exterior angle (i.e., supplementary to the interior angle) has a measure of degrees, with the sum of the exterior angles equal to 360 degrees or 2π radians or one full turn. As n approaches infinity, the internal angle approaches 180 degrees. For a regular polygon with 10,000 sides (a myriagon) the internal angle is 179.964°. As the number of sides increase, the internal angle can come very close to 180°, and the shape of the polygon approaches that of a circle. However the polygon can never become a circle. The value of the internal angle can never become exactly equal to 180°, as the circumference would effectively become a straight line. For this reason, a circle is not a polygon with an infinite number of sides. Diagonals For n > 2, the number of diagonals is ; i.e., 0, 2, 5, 9, ..., for a triangle, square, pentagon, hexagon, ... . The diagonals divide the polygon into 1, 4, 11, 24, ... pieces . For a regular n-gon inscribed in a unit-radius circle, the product of the distances from a given vertex to all other vertices (including adjacent vertices and vertices connected by a diagonal) equals n. Points in the plane For a regular simple n-gon with circumradius R and distances di from an arbitrary point in the plane to the vertices, we have For higher powers of distances from an arbitrary point in the plane to the vertices of a regular -gon, if , then , and , where is a positive integer less than . If is the distance from an arbitrary point in the plane to the centroid of a regular -gon with circumradius , then , where = 1, 2, …, . Interior points For a regular 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