Regular polygon common angle is a constructible number—that is, can be written in terms of the four basic arithmetic operations and the extraction of square roots. A "regular skew polygon" in 3-space can be seen as nonplanar paths zig-zagging between two parallel planes, defined as the side-edges of a uniform antiprism. All edges and internal angles are equal. More generally "regular skew polygons" can be defined in "n"-space. Examples include the Petrie polygons, polygonal paths of edges that divide a regular polytope into two halves, and seen as a regular polygon in orthogonal projection. In the infinite limit "regular skew polygons" become
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