Editing Regular polyhedron (section)

{{Short description|Polyhedron with regular congruent polygons as faces}}
A '''regular polyhedron''' is a [[polyhedron]] whose [[symmetry group]] acts [[transitive group action|transitively]] on its [[Flag (geometry)|flag]]s. 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 the faces are [[Congruence (geometry)|congruent]] [[regular polygon]]s which are assembled in the same way around each [[vertex (geometry)|vertex]].

A regular polyhedron is identified by its [[Schläfli symbol]] of the form {''n'', ''m''}, where ''n'' is the number of sides of each face and ''m'' the number of faces meeting at each vertex. There are 5 finite convex regular polyhedra (the [[Platonic solid]]s), and four regular [[star polyhedra]] (the [[Kepler–Poinsot polyhedra]]), making nine regular polyhedra in all. In addition, there are five regular compounds of the regular polyhedra.