Regular polytope impossible ("not constructible"). The simplest few regular polygons that are impossible to construct are the "n"-sided polygons with "n" equal to 7, 9, 11, 13, 14, 18, 19, 21... Constructibility in this sense refers only to ideal constructions with ideal tools. Of course reasonably accurate approximations can be constructed by a range of methods; while theoretically possible constructions may be impractical. Euclid's "Elements" gave what amount to ruler-and-compass constructions for the five Platonic solids. (See, for example, Euclid's Elements.) However, the merely practical question of how one might draw a straight line in space, even with a ruler, might lead
Regular polygon coprime, or the figure will degenerate. The degenerate regular stars of up to 12 sides are: Depending on the precise derivation of the Schläfli symbol, opinions differ as to the nature of the degenerate figure. For example, {6/2} may be treated in either of two ways: All regular polygons are self-dual to congruency, and for odd "n" they are self-dual to identity. In addition, the regular star figures (compounds), being composed of regular polygons, are also self-dual. A uniform polyhedron has regular polygons as faces, such that for every two vertices there is an isometry mapping one into the other