Fig. 457.30A Axes of Rotation of Icosahedron: A. The rotation of the icosahedron on axes through midpoints of opposite edges define 15 great-circle planes. B. The rotation of the icosahedron on axes through opposite vertexes define six equatorial great-circle planes, none of which pass through any vertexes. C. The rotation of the icosahedron on axes through the centers of opposite faces define ten equatorial great-circle planes, which do not pass through any vertexes.