Sphere two poles is called the axis of rotation. Circles on the sphere that are parallel to the equator are lines of latitude. This terminology is also used for such approximately spheroidal astronomical bodies as the planet Earth (see geoid). Any plane that includes the center of a sphere divides it into two equal hemispheres. Any two intersecting planes that include the center of a sphere subdivide the sphere into four lunes or biangles, the vertices of which all coincide with the antipodal points lying on the line of intersection of the planes. The antipodal quotient of the sphere is the
Exotic sphere Similar manifolds are called Brieskorn spheres. Given an (orientation-preserving) diffeomorphism , gluing the boundaries of two copies of the standard disk "D" together by "f" yields a manifold called a "twisted sphere" (with "twist" "f"). It is homotopy equivalent to the standard "n"-sphere because the gluing map is homotopic to the identity (being an orientation-preserving diffeomorphism, hence degree 1), but not in general diffeomorphic to the standard sphere. Setting formula_25 to be the group of twisted "n"-spheres (under connect sum), one obtains the exact sequence For , every exotic "n"-sphere is diffeomorphic to a twisted sphere, a result proven by