I intend to turn a large hollow wooden sphere on a lathe. To do this, I need to construct a roughly spherical hollow wooden blank. An icosadodecahedron seems like a good choice, as it is pretty close to spherical and would be an easy solid to construct. (All edges are the same length and have the same dihedral angle.) An icosahedron would also work, but has sharper apex angles and would thus require thicker wood. What I am unable to figure out is two formulas. The first is to compute the edge length of the polygons required for a nested sphere of a given diameter. The second is for the distance of the centers of the polygons from the center of the nested sphere. That would let me compute the thickness of the wood required.
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