Symmetry sphere for icosahedron

31 great circles compose this sphere. 6 of them are perpendicular to the axes of opposite regular icosahedron vertices, 10 perpendicular to the axes of opposite face centers, and 15 perpendicular to the axes of opposite the edge centers. Note that the symmetry sphere for the regular dodecahedron is identical, because the icosahedron and dodecahedron are duals. The vertices of the regular cube, octahedron, and tetrahedron can also be found in the intersections of these great circles. The size is 75mm in diameter, with 1mm diameter wires.