Chapter 6.2, Problem 47MS

Here we celebrate the power of algebra as a powerful way of finding unknown quantities by naming them, of expressing infinitely many relationships and connecions clearly and succinctly, and of uncovering pattern and structure.

The other football. You have a solid with $n(n^2-1)$ vertices, $n^3+6n+2$ edges, and $8n$ faces. Use the Euler Characteristic to solve for n. Find the number of vertices, edges, and faces of your solid. (Can you think of a solid with these values?)