Question

Given a polyhedron has 6 vertices and 10 edges. How many faces does the polyhedron have.

Answer 1

According to the Euler's formula:

$F+V-E=2$

Where

$\begin{gathered} F=\text{ the number of faces} \\ V=\text{ the number of vertices} \\ E=\text{ the number of edges} \end{gathered}$

In this case,

$\begin{gathered} V=6 \\ E=10 \end{gathered}$

Substituting V = 6 and E = 10 into Euler's formula, it follows that:

$\begin{gathered} F+6-10=2 \\ F-4=2 \\ F=2+4=6 \end{gathered}$

Therefore, the polyhedron has 6 faces.

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