Uniform Polyhedron

+A uniform polyhedron is a three-dimensional shape characterized by two key properties: all its faces are [Regular Polygon](/wiki/regular_polygon)s (which can be [Convex Polygon](/wiki/convex_polygon)s or [Star Polygon](/wiki/star_polygon)s), and all its [Vertex](/wiki/vertex)s are identical. The condition of identical vertices means that the polyhedron is [Vertex-transitive](/wiki/vertex-transitive); for any two vertices, there is a [Symmetry](/wiki/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 Solid](/wiki/platonic_solid)s and [Archimedean Solid](/wiki/archimedean_solid)s, as well as an infinite family of [Prism](/wiki/prism)s and [Antiprism](/wiki/antiprism)s. Non-convex uniform polyhedra, known as [Star Polyhedron](/wiki/star_polyhedron)s, also exist, such as the [Kepler-Poinsot Solid](/wiki/kepler-poinsot_solid)s.

+The duals of uniform polyhedra are [Face-transitive](/wiki/face-transitive) polyhedra, meaning all their faces are identical, though not necessarily regular polygons.

+- [Vertex-transitive](/wiki/vertex-transitive)

+A uniform polyhedron is a three-dimensional shape where all its faces are regular polygons and all its [Vertex](/wiki/vertex)s are identical. This geometric harmony means every vertex looks the same, and all faces are [Regular Polygon](/wiki/regular_polygon)s, creating a balanced and symmetrical form.

+## See also

+- [Polyhedron](/wiki/polyhedron)

+- [Platonic Solid](/wiki/platonic_solid)

+- [Archimedean Solid](/wiki/archimedean_solid)