Specific face of a solid identified for the purpose of providing a measure or a definition.
Certain solids do not have a base in the strict sense of the word. This is the case with spheres, most Platonic solids, bipyramids, etc.
Examples
In this illustration, the polygon on which each triangular lateral face rests is called the base of the pyramid. In this case, it is a pentagon. Therefore, the pyramid is called a pentagonal pyramid.
In this illustration, the base of the cylinder is a circle of radius r.