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
Riemann sphere that group is called SO(3). In this sense, this is by far the most symmetric metric on the sphere. (The group of all isometries, known as O(3), is also 3-dimensional, but unlike SO(3) is not a connected space.) Conversely, let "S" denote the sphere (as an abstract smooth or topological manifold). By the uniformization theorem there exists a unique complex structure on "S", up to conformal equivalence. It follows that any metric on "S" is conformally equivalent to the round metric. All such metrics determine the same conformal geometry. The round metric is therefore not intrinsic to the Riemann sphere,