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
Great dodecahemidodecahedron Great dodecahemidodecahedron In geometry, the great dodecahemidodecahedron is a nonconvex uniform polyhedron, indexed as U. Its vertex figure is a crossed quadrilateral. It is the only nonconvex uniform polyhedron whose faces are all non-convex regular polygons (star polygons), namely the star polygons {/} and {/}, besides the regular small stellated dodecahedron {/,5} and great stellated dodecahedron {/,3}. It is a hemipolyhedron with 6 decagrammic faces passing through the model center. Its convex hull is the icosidodecahedron. It also shares its edge arrangement with the great icosidodecahedron (having the pentagrammic faces in common), and with the great icosihemidodecahedron (having the decagrammic