= Uniform polyhedron
A uniform polyhedron has regular polygonal faces and a symmetry group acting transitively on its vertices. Thus every vertex has the same surrounding face pattern, but that pattern may use more than one regular polygon type. The definition includes both convex examples and, under the broader convention, star-faced or self-intersecting examples.
A <cube> is uniform: each vertex meets three congruent squares, and its <rotational symmetries> carry any vertex to any other. A <cuboctahedron> has triangles and squares, alternating around every vertex, and is also uniform. Uniformity does not require every pair of faces to be related by a symmetry; that stronger face condition distinguishes regular solids.
The requirement is geometric. Merely drawing a polyhedron with the same number of incident edges at every vertex does not ensure regular faces or a vertex-transitive symmetry group. Regular <prisms> and regular <antiprisms> supply infinite families of convex uniform polyhedra.
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