A polyhedron has 6 faces and 4 vertices. Use Euler's formula to calculate the number of edges.

Euler said:

V + F - E = 2
so if
4 + 6 - E = 2
-E = -8
E = 8

It has 8 edges

Euler's formula states that for any polyhedron, the number of faces (F), vertices (V), and edges (E) are related by the equation F + V - E = 2.

Given that the polyhedron in question has 6 faces (F) and 4 vertices (V), we can substitute these values into the equation:

6 + 4 - E = 2

Now, let's solve for E:

10 - E = 2

Subtracting 10 from both sides:

-E = -8

Multiplying both sides by -1:

E = 8

Therefore, the polyhedron has 8 edges.

Euler's formula, named after the Swiss mathematician Leonhard Euler, relates the number of faces (F), vertices (V), and edges (E) in a polyhedron. The formula states that F + V - E = 2.

Now, to calculate the number of edges in the given polyhedron with 6 faces and 4 vertices, we can use Euler's formula. Let's substitute the values into the formula:

6 + 4 - E = 2

Simplifying the equation:

10 - E = 2

To isolate E, we subtract 10 from both sides of the equation:

-E = 2 - 10
-E = -8

Finally, we multiply both sides of the equation by -1 to find the positive value of E:

E = 8

Therefore, the polyhedron has 8 edges.