Question

A tetrahedron has $4$ faces and $6$ edges. How many vertices does it have?

Answer 1

As we know for any polyhedron that doesn't intersect itself,

$V-E+F=2$

Where ,

$V$ is number of vertices $=?$

$E$ is number of edges $=6$

$F$ is number of faces $=4$

So we have,

$$\begin{gathered} V-E+F=2 \\ \Rightarrow V-6+4=2 \\ \Rightarrow V-2=2 \\ \Rightarrow V=2+2 \\ \Rightarrow V=4 \end{gathered}$$

Hence, given tetrahedron have $4$ vertices.