A square based pyramid fits the given description
sphere
A triangular pyramid.
Triangular prism of course!
A quadrilateral based pyramid.
A hexahedron, also known as a parallelepiped.
sphere
A hemisphere
The solid figure that has the same number of faces and vertices and has 8 edges is a cube. A cube has 6 faces, 8 vertices, and 12 edges, so it fits the description given.
6
A Cylinder.
cube
It is a sphere
none
A tetrahedron.
Pyramid
square
A triangular pyramid.