A sphere is a perfectly round object, like a child's bouncing ball. It has only one face, so there are no edges, which occur when two faces meet.
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There are infinitely many spatial figures and it is not possible to give a comprehensive answer. For a partial answer, see the following link. However, the link is concerned only with polyhedra. There are other spatial figures - like spheres and ellipsoid etc.
The number of edges and vertices ina polyhedron will depend on the polyhedron one selects either to study, build or etc...
A "pyramid" is a non-specific term refering to a 3-d shape consisting of a base which is a polygon with n sides, and n triangular faces meeting at an apex. Such a pyramid would have 2n edges. Thus, a triangular pyramid (tetrahedron) has 6 edges; a square based pyramid has 8, etc.
There are many possible answers: A cylinder A cone sliced by two planes perperndicular to its axis A toroid (doughnut) sliced by a plane vertical to its axis. A sphere sliced by two planes An ellipsoid sliced by two planes A paraboloid sliced by two planes etc.
Depends whether you want the formula for surface area, volume, perimeter, size of sphere it would fit into etc... Please clarify next time.