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 skew apeirohedron Regular skew apeirohedron In geometry, a regular skew apeirohedron is an infinite regular skew polyhedron, with either skew regular faces or skew regular vertex figures. According to Coxeter, in 1926 John Flinders Petrie generalized the concept of regular skew polygons (nonplanar polygons) to finite regular skew polyhedra in 4-dimensions, and infinite regular skew apeirohedra in 3-dimensions (described here). Coxeter identified 3 forms, with planar faces and skew vertex figures, two are complements of each other. They are all named with a modified Schläfli symbol {"l","m"|"n"}, where there are "l"-gonal faces, "m" faces around each vertex, with "holes" identified as "n"-gonal