1. Infinite-dimensional sphere by identifying each pair of antipodal points . 2. Any two antipodal points on the Poincar?sphere refer to orthogonal polarization states. 3. It is understood that antipodal points on the equator represent a single line. 4. The requirement to pass at least two antipodal points causes some problems in route planning. 5. It can be seen that the route does not pass through any pairs of antipodal points . 6. Identifying and amounts to identifying with, which in turn amounts to identifying antipodal points on. 7. The exception is a pair of antipodal points , for which there are infinitely many great circles. 8. Any two great circles intersect precisely in two antipodal points ( identified in the projective plane ). 9. As a antipodal points where the axis of this theoretical dipole intersects the Earth's surface. 10. An impact event may cause a mantle plume ( volcanism ) at the antipodal point of the impact.
