What is the difference of the face and base?

Answer 1

These are terms which are used in the context of polyhedra. A polyhedron is a 3-dimensional, solid shape which is bounded by polygons. Every such polygon is a face. However, some faces are also called bases and this depends on the polyhedron.

All the faces of a pyramid, with the possible exception of one, are triangles. The one different face is called the base. In a triangular pyramid (tetrahedron) the face that is at the bottom is the base.

A prism has two identical, parallel faces which may be any polygon. All the other faces are rectangles. A non-rectangular faces are called the bases. In a cuboid all six faces are rectangles and so any pair of opposite faces are called bases.