Thread: Rectangular Prisms

/ = Division
= = Equals
*= Multiplication

Earlier in the year, we did Rectangular Prisms. First, we just counted the Faces, Vertices, and Edges. Of course, we did it with other objects, but I have a simple question about rectangular prisms.

Now, while counting up all of these Faces, Vertices, and Edges, I came across a pattern!

It seemed like the following equation kept showing up, no matter what the object looked like (as long as it was still a rectangular prism, of course):
(V/2)*3=E
and vise-versa, being
(E/3)*2=V

Some objects I drew up had the follwing results, which all seemed to follow my equation:
Object 1
(Basic Cube)
F=6
V=8
E=12
Object 2
F=8
V=12
E=18
Object 3
F=12
V=20
E=30

And there's the whole F+V=E+2 thing
But does anybody know of any relationship from
F->V or
F->E

It's nothering me, because I am just so curious about whether there is some connection there? Thanks in advance to any replies!

Originally Posted by Yuripro84

/ = Division
= = Equals
*= Multiplication

Earlier in the year, we did Rectangular Prisms. First, we just counted the Faces, Vertices, and Edges. Of course, we did it with other objects, but I have a simple question about rectangular prisms.

Now, while counting up all of these Faces, Vertices, and Edges, I came across a pattern!

It seemed like the following equation kept showing up, no matter what the object looked like (as long as it was still a rectangular prism, of course):
(V/2)*3=E
and vise-versa, being
(E/3)*2=V

Some objects I drew up had the follwing results, which all seemed to follow my equation:
Object 1
(Basic Cube)
F=6
V=8
E=12
Object 2
F=8
V=12
E=18
Object 3
F=12
V=20
E=30

And there's the whole F+V=E+2 thing
But does anybody know of any relationship from
F->V or
F->E

It's nothering me, because I am just so curious about whether there is some connection there? Thanks in advance to any replies!

I will not go into any research or what. I will just rely on your findings here.
So, let us say your findings are correct, then,

(V/2)*3=E
and vise-versa, being
(E/3)*2=V

Both of which simplify to
3V = 2E ------------------(1)

And,
F+V = E+2 ---------------(2)

You want to know the relation of F and V, or F and E.

From the Equations (1) and (2) we can find these relations.

For the F and V:
EXpress the E in terms of V in Eq.(2).
So, from (1),
E = 3V/2
Substitute that into (2),
F +V = (3V/2) +2
Blah, blah, blah...
F = (V/2) +2 -----------------(3). There you are.

Try getting the relation of F and E that way.
You should get
F = (E/3) +2 ---------------(4)

That is it.

Thanks man, those worked for all of my examples, I didn't think it was possible