What is Regular polytope?
[[Image:POV-Ray-Dodecahedron.svg|right|thumb|A [[dodecahedron]], one of the five [[Platonic solid]]s]] In [[mathematics]], a '''regular polytope''' is a shape with sides and [[vertices]] that are [[symmetrical]]. Like other [[polytope]]s, regular polytopes are found in any number of [[dimension]]s. A [[two-dimensional]] regular polytope is a [[regular polygon]], and a [[three-dimensional]] regular polytope is a '''regular [[polyhedron]]'''. Even though these groups include different shapes, they are based on the same idea of the shapes having regular symmetry. Regular polytopes have regular facets (faces, as seen from the 3D viewpoint), and their [[vertex figure]]s are regular. Each number of dimensions has a different set of regular polytopes. However, all of them have a simple shape. The simplest of regular polytopes is the [[triangle]] in 2D, the [[tetrahedron]] in 3D, and the [[pentachoron]] in 4D. {{Polytopes}} {{math-stub}} [[Category:Shapes]]