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

rotating dodecahedron

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

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

4 Answers 4

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

enter image description here

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]
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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}]

enter image description here

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I suggest you start with

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.

dodecahedron

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.

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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[%]

enter image description here

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    $\begingroup$ N[PolyhedronData["Dodecahedron", "Vertices"]] is fine, too. $\endgroup$ Apr 26, 2020 at 8:46

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