Help with Problem Investigating Structures Made of Unit Rods

[Carlito1]

Hey. I’m having trouble with this work I’ve been set about structures. I understand some of it, which I’ll explain later, but I really need your help with it!

My task is to investigate different sized cubes, made up of single unit rods and justify formulae for the number of rods and joints in the cubes. For example, 2 by 2 by 2 cube, 3 by 3 by 3 cube etc etc etc…

I desperately need help on getting a formula to work this out. I know already, as my teacher gave us these results, that a 1 by 1 by 1 cube has the following:

8 Three-Joints ( as do all cubes)
0 Four Joints
0 Five Joints
0 Six Joints

and a 2 by 2 by 2 has:

8 three joints
12 four joints
2 five joints
1 six joints

I really need a formula in order to calculate how many joints a 3 by 3 by 3 has, and with that formula to use it on let's say a 55 by 55 by 55 cube.

All help would be appreciated!

 

[Carlito1]

Sorry for being confusing, but here's the task:

Sorry, I was vague.
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Rigid Structures are constructed using unit rods.

An example is shown below:

* Pic opf a 2 by 2 by 2 cube*

The individual rods in the structures are held together using different types of joints. (Just think of making cubes using matchsticks and playdough*.

http://img61.imageshack.us/img61/6166/joints3lz.jpg

A three joint would be on the vertices of each cube no matter what the size and so therefore there'll be 8 three-joints.