Question

Using Euler’s formula, how many edges does a polyhedron with 9 faces and 14 vertices have? Thank you

Answer 1

`F+V=E+2`

Solve the Euler's formula above to E (Edges)

`\begin{gathered} \text{Substract 2 in both sides of the equation;} \\ \\ F+V-2=E+2-2 \\ F+V-2=E \\ \\ \text{ Rewrite the equation:} \\ \\ E=F+V-2 \end{gathered}`

Use the given data;

Faces; F=9

Vertices: V=14

`\begin{gathered} E=9+14-2 \\ E=21 \end{gathered}`

The polyhedron has 21 edges