Pearson Geometry Common Core, 2011
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Pearson Geometry Common Core, 2011 View details
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Exercise 7 Page 752

Euler's Formula states that the sum of the number of faces and vertices of a polyhedron is two more than the number of its edges.

8

Practice makes perfect

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
6+ x= 12+2
6+x=14
x=8

We found that the polyhedron has 8 vertices.