For the bigger-is-better type student, the 10 universities with the largest undergraduate populations in fall 2013 enrolled an average of 43,186 students. Among the 1,248 ranked universities responding to an annual U.S. News survey, the average was 6,154.
In geometry, a vertex (plural vertices) is a special kind of point that describes the corners or intersections of geometric shapes.
A solid figure is a three dimensional shape. A polyhedron is three dimensional shape having straight lines. You may have thought all shapes are polyhedrons, but not all shapes are. Spheres among other things are not polyhedrons.