How can I find the normals of a Dodecahedron in rational numbers?

[TheDestroyer]

Hello guys,

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.

 

[fresh_42]

I'm afraid there is no way other than calculate the equations of all faces.