Question

Can a polyhedron have 12 faces, 22 edges and 17 vertices?

Answer 1

Answer:

No polyhedron has 12 faces, 22 edges, and 17 vertices.

Step-by-step explanation:

Consider the provided information.

It is given that we need to make a polyhedron having 12 faces, 22 edges and 17 vertices.

According to Euler's polyhedron formula:

V - E + F = 2

Where V is the number of vertices, E is the number of edges and F is the number of faces.

Now, simply substitute the number of faces, edges, and vertices in the above formula.

$17-22+12=2$

$29-22=2$

$7=2$

Which is not true.

Thus, No polyhedron has 12 faces, 22 edges, and 17 vertices.