# How can I obtain and work with a Platonic dodecahedron?

I want to obtain and work with a Platonic dodecahedron like this one:

I don't have basic knowledge needed to do it. Can anyone can help me? Just the basics to get me started.

• Can you elaborate the parts you consider essential; is it about the animation, specific visualization (which features?) or what? May 5, 2019 at 15:39

R = PolyhedronData["Dodecahedron", "BoundaryMeshRegion"]


See the documentations of MeshRegion and BoundaryMeshRegion in order to learn how to work extract information from it.

Most notable properties are the vertex coordinates

MeshCoordinates[R]


and the index list for the faces

MeshCells[R,2]


The edge can be obtained with

MeshCells[R,1]


Dodecahedron comes as a built-in object in Mathematica (version 12; replacing Dodecahedron[] with PolyhedronData["Dodecahedron", "BoundaryMeshRegion"] works in older versions), which makes this pretty easy.

For the animation, you can start with the following (click for animation):

Animate[
Graphics3D[
{EdgeForm[Thick], FaceForm[Opacity[3/4]], Dodecahedron[]},
Boxed -> False, SphericalRegion -> True,
ViewPoint -> 5 {Sin[a], Cos[a], 1/2}],
{a, 0, 2 Pi}]


PolyhedronData["Dodecahedron"]


That will return a 3D plot of Platonic dodecahedron. When you click on the selection bar on the righthand side of the plot, the Suggestion Bar should appear. It will give a lot options to experiment with.

You can see the Suggestion Bar at the bottom of the above screen shot. Each of the tags along the bottom are menus that will give commands to explore.

If you just need the vertices, you can use the much more general function SpherePoints:

SpherePoints[20]

(*    {{-0.187592, -0.57735, -0.794654}, {-0.187592, 0.57735, -0.794654},
{0.187592, -0.57735, 0.794654}, {0.187592, 0.57735, 0.794654},
{-0.607062, 0., -0.794654}, {0.607062, 0., 0.794654},
{-0.303531, -0.934172, -0.187592}, {-0.303531, 0.934172, -0.187592},
{0.303531, -0.934172, 0.187592}, {0.303531, 0.934172, 0.187592},
{-0.491123, -0.356822, 0.794654}, {-0.491123, 0.356822, 0.794654},
{0.491123, -0.356822, -0.794654}, {0.491123, 0.356822, -0.794654},
{-0.794654, -0.57735, 0.187592}, {-0.794654, 0.57735, 0.187592},
{0.794654, -0.57735, -0.187592}, {0.794654, 0.57735, -0.187592},
{-0.982247, 0., -0.187592}, {0.982247, 0., 0.187592}}    *)

ConvexHullMesh[%]


• N[PolyhedronData["Dodecahedron", "Vertices"]] is fine, too. Apr 26, 2020 at 8:46