Question

Use Euler’s formula to find the number of vertices in a polyhedron with 6 square faces and 12 edges

Answer 1

`V = 8`

Explanation:

we know that

The Euler's formula state that: In a polyhedron, the number of vertices, minus the number of edges, plus the number of faces, is equal to two

`V - E + F = 2`

in this problem we have

`V=?\\E=12\\F=6`

substitute the given values

`V - 12 + 6 = 2`

solve for V

Combine like terms left side

`V - 6 = 2`

Adds 6 both sides

`V - 6+6 = 2+6`

`V = 8`