Sphere ( 0 faces , 0 edges , 0 vertices )
A 3D shape that has 6 edges is called a hexagonal prism.
triangle
If they are all plane faces then there is no such figure. Otherwise it could be a sphere intersected by two planes, an ellipsoid intersected by two planes, a cone intersected by two planes, or one of several other shapes.
corners of a 3d shape
sphere
A cube
A cube
A pentagonal prism has 15 edges
Spherical
Sphere
It has 12 edges and 6 faces