Semiregular polyhedron

The term semiregular polyhedron (or semiregular polytope) is used variously by different authors. The term semiregular polyhedron (or semiregular polytope) is used variously by different authors. In its original definition, it is a polyhedron with regular faces and a symmetry group which is transitive on its vertices, which is more commonly referred to today as a uniform polyhedron (this follows from Thorold Gosset's 1900 definition of the more general semiregular polytope). These polyhedra include: These semiregular solids can be fully specified by a vertex configuration, a listing of the faces by number of sides in order as they occur around a vertex. For example, 3.5.3.5, represents the icosidodecahedron which alternates two triangles and two pentagons around each vertex. 3.3.3.5 in contrast is a pentagonal antiprism. These polyhedra are sometimes described as vertex-transitive. Since Gosset, other authors have used the term semiregular in different ways in relation to higher dimensional polytopes. E. L. Elte provided a definition which Coxeter found too artificial. Coxeter himself dubbed Gosset's figures uniform, with only a quite restricted subset classified as semiregular.