Question

Using Euler’s formula, how many edges does a polyhedron with 20 faces and 12 vertices have?

Answer 1

Euler's formula for a polyhedron is given by:

$\begin{gathered} F+V=E+2 \\ \text{where,} \\ F=\text{faces} \\ V=\text{vertices} \\ E=\text{edges} \end{gathered}$

Make E, the subject of the formula:

$\begin{gathered} F+V=E+2 \\ E=F+V-2 \end{gathered}$

Put F = 20, V = 12, to obtain E,

$\begin{gathered} E=20+12-2 \\ E=30 \end{gathered}$

Therefore, there are 30 edges