Question

A polyhedron has 14 faces and 46 edges how many vertices does it have?

Answer 1

Number of vertices are 34.

Explanation:

The relation between the number of vertices, number of edges and number of faces was given by Euler's formula, which is as under:

`F + V - E =2`

Where
`F` is the number of faces in the polyhedron.

`V` is the number of vertices in the polyhedron and

`E` is the number of edges in the polyhedron.

Let us try to apply this formula in a cube. We know that number of vertices are 8, number of edges are 12 and number of faces are 6.

6 + 8 - 12
`\Rightarrow 2`

Hence, the formula is applicable.

Applying Euler's formula in the given question.

F = 14

E = 46

V = ?

Using Euler's Formula:

`14 + V - 46 = 2 \\\Rightarrow V = 2 + 32\\\Rightarrow V = 34`

Hence, number of vertices are 34.