A uniform polyhedron is a three-dimensional shape characterized by two key properties: all its faces are Regular Polygons (which can be Convex Polygons or Star Polygons), and all its Vertexs are identical. The condition of identical vertices means that the polyhedron is Vertex-transitive; for any two vertices, there is a Symmetry operation that maps one to the other. This results in a high degree of geometric harmony and visual consistency across the entire shape.
Uniform polyhedra encompass a broad range of highly symmetrical polyhedra. This class includes the well-known Platonic Solids and Archimedean Solids, as well as an infinite family of Prisms and Antiprisms. Non-convex uniform polyhedra, known as Star Polyhedrons, also exist, such as the Kepler-Poinsot Solids.
The duals of uniform polyhedra are Face-transitive polyhedra, meaning all their faces are identical, though not necessarily regular polygons.
