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
Euclidean tilings by convex regular polygons figures, which are also called "m"-Archimedean tilings. For edge-to-edge Euclidean tilings, the internal angles of the polygons meeting at a vertex must add to 360 degrees. A regular -gon has internal angle formula_1 degrees. There are seventeen combinations of regular polygons whose internal angles add up to 360 degrees, each being referred to as a "species" of vertex; in four cases there are two distinct cyclic orders of the polygons, yielding twenty-one "types" of vertex. Only eleven of these can occur in a uniform tiling of regular polygons, given in previous sections. In particular, if three polygons meet at a