Editing Dodecahedron (section)

==Regular dodecahedron==
{{Main|Regular dodecahedron}}
The convex regular dodecahedron is one of the five regular [[Platonic solid]]s and can be represented by its [[Schläfli symbol]] {5,3}.

The [[dual polyhedron]] is the regular [[icosahedron]] {3,5}, having five equilateral triangles around each vertex.

{| class=wikitable align=center
|+ Four kinds of regular dodecahedra
|- align=center
|[[File:Dodecahedron.png|x150px]]<br>Convex [[regular dodecahedron]]
|[[File:Small stellated dodecahedron.png|x150px]]<br>[[Small stellated dodecahedron]]
|[[File:Great dodecahedron.png|x150px]]<br>[[Great dodecahedron]]
|[[File:Great stellated dodecahedron.png|x150px]]<br>[[Great stellated dodecahedron]]
|}
The convex regular dodecahedron also has three [[stellation]]s, all of which are regular star dodecahedra. They form three of the four [[Kepler–Poinsot polyhedron|Kepler–Poinsot polyhedra]]. They are the [[small stellated dodecahedron]] {{{sfrac|5|2}},5}, the [[great dodecahedron]] {5,{{sfrac|5|2}}}, and the [[great stellated dodecahedron]] {{{sfrac|5|2}},3}. The small stellated dodecahedron and great dodecahedron are dual to each other; the great stellated dodecahedron is dual to the [[great icosahedron]] {3,{{sfrac|5|2}}}. All of these regular star dodecahedra have regular pentagonal or [[pentagram]]mic faces. The convex regular dodecahedron and great stellated dodecahedron are different realisations of the same [[abstract polytope|abstract regular polyhedron]]; the small stellated dodecahedron and great dodecahedron are different realisations of another abstract regular polyhedron.