Hemisphere

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 surface called the real projective plane, which can also be thought of as the northern hemisphere with antipodal points of the equator identified. The round hemisphere is conjectured to be the optimal (least area) filling of the Riemannian circle. The circles of intersection of any plane not intersecting the sphere's center and the sphere's surface are called spheric sections. [Sphere. Wikipedia]