This is my first attempt at using the fantastic Cabri-3D. In the probability store you can find this "distorted" die;

In fact I have found it on the net now here. My die was bought in the Village Games shop in Camden Market, London.

One of my students wrote her Maths Studies project on this die and as she wrote it I thought that may more mileage in the idea of analysing dice that were not regular. What about the centre of mass for example? Would its position play a role in the probability of each number being thrown or was the area of side more important? Probably (!) these two factors are related anyway. My guess is that this could have potential for an extended essay - could you create a viable model for the probability distibution from the geometry of the die?

I looked at the die and decided that it was based on a truncated pyramid - two of the opposite faces were similar and it seemed a nice each way to construct an irregular die. Then, armed with a demo copy of Cabri 3D, I set about modelling such a construction. Below is what I have come up with although to see it at all you will need to download the demo version of Cabri 3D from here or here. Better still, buy it. It is awesome.

Once you have the software in place (installing Cabri 3D on your computer automatically installs the plug-in you need to view this page), drag the red dots to alter the distorted die. Right-click and drag to rotate the figure. Or you can use Cabri 3D to open and alter the original file. Use Ctrl+M to see the hidden constructions. Better still, do Document->Add Net Page to create a net of your die to print out. You could then use it as a template to build a die of your own. I have put in the diagonals of the die for you to see if they intersect in one place or not. Have fun!