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
Simplicial sphere "i"-faces of any simplicial "d"-sphere with "f" = "n" vertices. This conjecture was proved for polytopal spheres by Peter McMullen in 1970 and by Richard Stanley for general simplicial spheres in 1975. The g"-conjecture, formulated by McMullen in 1970, asks for a complete characterization of "f"-vectors of simplicial "d"-spheres. In other words, what are the possible sequences of numbers of faces of each dimension for a simplicial "d"-sphere? In the case of polytopal spheres, the answer is given by the g"-theorem, proved in 1979 by Billera and Lee (existence) and Stanley (necessity). It has been conjectured that the same conditions