Calculating Vertices & Edges on a Cube - Geometry for Beginners

[Bashyboy]

Hi, I was wondering how to calculate, mathematically, the number of vertices on a cube, rather than just count them? Also, in a cube, how many edges are shared by a face? By counting the number of edges, there comes out to be 24, but since it face shares four edges, shouldn't there be 6 edges then? I am trying to calculate both of these without counting. I am reading geometry for beginners by G. A. Hill, written in 1884; it is profoundly interesting, but since I never took geometry, I just don't have an intuition for it. Is there perhaps a simpler book that someone could suggest, for now to read?

 

[piknless]

Ah yes, I remembering learning about this a long time ago, you have a formula along the lines of F+V-E=2. This is Euler's formula, where F= the number of faces, V= the number of vertices, and E=the number of edges. So you can solve for the third one by knowing the other two.