Question

The sum of the number of edges and vertices of the polyhedron is ________.

Answer 1

Look at the net of the given polyhedron.

Answer 2

tips?

Answer 3

Start counting :P

Answer 4

it has 8 faces

Answer 5

since it seems to be a prism, it should have 24 edgess

Answer 6

Oh wait, those fold together. It's not quite as simple as I thought it would be.

Answer 7

so is it a pyramid?

Answer 8

if so, the edges equal 16

Answer 9

I'm not sure what exactly you would call the shape, but I will tell you there are fewer than 16 edges.

Answer 10

For now, only look at the triangle at the top and bottom of the diagram. These both have 3 edges, and they won't have any sharing edges.

Answer 11

k

Answer 12

However, the they will share some edges with the row of triangles in the middle. In particular, they will share the all of the edges on the top and bottom of that row.

Answer 13

k

Answer 14

That means we have 6 edges so far, and we've already counted the edges on the top.bottom triangle, and all the edges on the top/bottom of the row of triangles.

The only edges we have left to count are those drawn diagonally in the middle row of triangles.

Answer 15

k

Answer 16

There are 7 edges there. However, the outer edge will be shared, so we subtract 1. This gives us \(6+6=12\) edges.

Answer 17

ok

Answer 18

how about vertices?

Answer 19

Give me a minute more to make sure, but I think it would just be 6 vertices.

Answer 20

12+6=18

Answer 21

wait

Answer 22

use Euler's formla

Answer 23

8+6-2=12

Answer 24

Euler's formula is Faces plus vertices minus edges=2

Answer 25

so you are right

Answer 26

I believe, when you fold this up you will get an octahedron. So if you need more confirmation, just look at the handy dandy picture here http://en.wikipedia.org/wiki/Octahedron

And Euler's formula is a much better approach than just counting.

Answer 27

k

Answer 28

ty

Answer 29

you're welcome.