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I need the normals of a Dodecahedron (fully symmetric 12 facets' polyhedron) given in rational numbers. I got tired searching the internet for that, so I expect something like:

{-Sqrt[1 + 2/Sqrt[5]], 0, 1/2 Sqrt[1/10 (5 - Sqrt[5])]]}

I tried Mathematica, but it gives 20 Faces for a Dodecahedron!!! Apparently there are repeated facets and it uses some systematic way to draw the Dodecahedron. The code I use to get the Facets in Mathematica is:

PolyhedronData["Dodecahedron", "Faces"]

Any help is highly appreciated.

Thanks.

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# Normals of a Dodecahedron

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