Regular polyhedron a hemisphere, and vertices around a great circle. It is "regular" if the vertices are equally spaced. The hosohedron {2,"n"} is dual to the dihedron {"n",2}. Note that when "n" = 2, we obtain the polyhedron {2,2}, which is both a hosohedron and a dihedron. All of these have Euler characteristic 2. Regular polyhedron A regular polyhedron is a polyhedron whose symmetry group acts transitively on its flags. A regular polyhedron is highly symmetrical, being all of edge-transitive, vertex-transitive and face-transitive. In classical contexts, many different equivalent definitions are used; a common one is that faces are congruent regular polygons
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