If a polyhedron has 13 vertices and 21 faces, how many edges does it have? I can't figure this one out.
Use Euler's formula which says that
V+F=E+2
where
V=vertices
F=faces
E=edges
For example, a cube has 8 vertices, 6 faces and 12 edges, so
8+6=12+2
ok thanks!!
You're welcome!
For a given polyhedron, there are 24 vertices and 32 faces. How many edges does the polyhedron have? [Hint: V + F = E + 2.]
To determine the number of edges in a polyhedron, you can use Euler's formula, which states that for any polyhedron, the number of vertices (V), edges (E), and faces (F) are related by the equation: V - E + F = 2.
In this case, you are given that the polyhedron has 13 vertices (V) and 21 faces (F). We can plug these values into Euler's formula to solve for the number of edges (E).
V - E + F = 2
13 - E + 21 = 2
Now, we can solve for E:
13 + 21 - 2 = E
32 = E
Therefore, the polyhedron must have 32 edges.