Regular polygon Regular polygon In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may be either convex or star. In the limit, a sequence of regular polygons with an increasing number of sides approximates a circle, if the perimeter or area is fixed, or a regular apeirogon (effectively a straight line), if the edge length is fixed. "These properties apply to all regular polygons, whether convex or star." A regular "n"-sided polygon has rotational symmetry of order "n". All vertices of a regular
Regular polytope one to question what exactly it means to "construct" a regular polyhedron. (One could ask the same question about the polygons, of course.) The English word "construct" has the connotation of systematically building the thing constructed. The most common way presented to construct a regular polyhedron is via a fold-out net. To obtain a fold-out net of a polyhedron, one takes the surface of the polyhedron and cuts it along just enough edges so that the surface may be laid out flat. This gives a plan for the net of the unfolded polyhedron. Since the Platonic solids have only triangles,