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
Petrie polygon of Petrie polygons was later extended to semiregular polytopes. The Petrie polygon of the regular polyhedron {"p", "q"} has "h" sides, where The regular duals, {"p","q"} and {"q","p"}, are contained within the same projected Petrie polygon. The regular Kepler–Poinsot polyhedra have hexagonal, {6}, and decagrammic, {10/3}, Petrie polygons. Infinite regular skew polygons (apeirogon) can also be defined as being the Petrie polygons of the regular tilings, having angles of 90, 120, and 60 degrees of their square, hexagon and triangular faces respectively. Infinite regular skew polygons also exist as Petrie polygons of the regular hyperbolic tilings, like the order-7 triangular