The azimuthal angle, the polar angle and the distance are the three variables in this shape's namesake coordinate system.
While transforming one of these objects to a different type of one of these objects without creasing, one can generate the Morin surface. Stephen Smale paradoxically showed that one can topologically evert one of these objects into itself. A manifold of this shape can be formed by taking a square region and identifying the two pairs of adjacent edges. Opposite points on these objects are called antipodes. The azimuthal angle, the polar angle and the distance are the three variables in this shape's namesake coordinate system. For 10 points, name these objects that have volume equal to four thirds pi times the radius cubed.
While transforming one of these objects to a different type of one of these objects without creasing, one can generate the Morin surface.
spheres [or 3-spheres]