Exercise 7 Page 752

Euler's Formula states that the sum of the number of faces F and vertices V of a polyhedron is two more than the number of its edges, E. F+ V= E+2 We are given that a polyhedron has 6 faces and 12 edges, and want to find the number of vertices. To do so, we will use Euler's Formula. Let x be the number of vertices. We will substitute the given information into the above formula and solve for x.

F+V=E+2

SubstituteValues

Substitute values

6+ x= 12+2

AddTerms

Add terms

6+x=14

SubEqn

LHS-6=RHS-6

x=8

We found that the polyhedron has 8 vertices.