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
N-sphere space and is an example of an -manifold. The volume form of an -sphere of radius is given by where is the Hodge star operator; see for a discussion and proof of this formula in the case . As a result, The space enclosed by an -sphere is called an -ball. An -ball is closed if it includes the -sphere, and it is open if it does not include the -sphere. Specifically: Topologically, an -sphere can be constructed as a one-point compactification of -dimensional Euclidean space. Briefly, the -sphere can be described as , which is -dimensional Euclidean space plus