Editing Regular polyhedron (section)

===Equivalent properties===

The property of having a similar arrangement of faces around each vertex can be replaced by any of the following equivalent conditions in the definition:

*The vertices of a convex regular polyhedron all lie on a [[sphere]].
*All the [[dihedral angle]]s of the polyhedron are equal
*All the [[vertex figure]]s of the polyhedron are [[regular polygon]]s.
*All the [[solid angle]]s of the polyhedron are congruent.<ref>{{cite book
  | last = Cromwell | first = Peter R. | title = Polyhedra | title-link = Polyhedra (book) | publisher = Cambridge University Press | year = 1997 | page = 77 | isbn = 0-521-66405-5 }}</ref>