Chapter 4.7, Problem 30MS

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

Triangular totaling. A tetrahedron is a 3-dimensional “triangle.” It has four faces, each a 2-dimensional triangle, and six edges. It turns out that a “triangle” in $\text{n - 1 dimensions has n}\left(\text{n - 1}\right)\text{/2 2-dimensional faces and n}\left(\text{n -1}\right)\left(\text{n -2}\right)\text{16 edges}\text{.}$

(Sec Mindscape 16.) Compute the number of edges and the number of 2-dimensional faces there are in a 5-dimensional triangle.