Question

If a solid shape has 12 faces and 20 vertices, then the number of edges in this solid is ______.

Answer 1

Step 1: Calculating the number of edges

It is given to us that, the number of faces are $12$, and the number of vertices are $20$

According to Euler's formula for a polyhedron,

$\mathrm{F}+\mathrm{V}-\mathrm{E}=2$

Here F= number of faces, E= number of edges, V= number of vertices.

$\therefore$The number of edges are:

$$\begin{gathered} \mathrm{F}+\mathrm{V}-\mathrm{E}=2 \\ \Rightarrow \mathrm{E}=\mathrm{F}+\mathrm{v}-2 \\ \Rightarrow \mathrm{E}=12+20-2 \\ \Rightarrow \mathrm{E}=32-2 \\ \Rightarrow \mathrm{E}=30 \end{gathered}$$

Therefore, If a solid shape has 12 faces and 20 vertices, then the number of edges in this solid is 30.