Question

A convex polyhedron has 6 vertices and 12 faces. How many edges does it have?

Answer 1

Answer:

16 edges.

Step-by-step explanation:

We will use Euler's polyhedron formula to solve for the edges of our convex polyhedron.

Euler's polyhedron formula is: $V+F-E=2$, where,

V= Vertices of polyhedron,

F= Faces of polyhedron,

E= Edges of polyhedron.

Let us substitute V=6 and F=12 in Euler's formula to find number of edges of our polyhedron.

$6+12-E=2$

$18-E=2$

Let us subtract 18 from both sides of our equation.

$18-E-18=2-18$

$-E=2-18$

$-E=-16$

$E=16$

Therefore, our convex polyhedron will have 16 edges.