Manipulate[Graphics3D[{Specularity[White, 20],
   Texture[ImageCrop[ExampleData[{"ColorTexture", "WhiteMarble"}], {128, 128}]],
   EdgeForm[Opacity[1/10]], (Append[#1, {VertexTextureCoordinates ->
     With[{n = Length[First[#1]]},
      Table[1/2 {Cos[2 [Pi] i/n], Sin[2 [Pi] i/n]} + {1/2, 1/2}, {i, 0, n - 1}]]}] &) /@
    Flatten[Normal[PolyhedronData[p, "Faces"]]]},
  Lighting -> "Neutral"], {{p, "RhombicHexecontahedron", "polyhedron"}, PolyhedronData[]}]