Designing a biased die (non-regular icosahedron)

Not an engineer. I may be asking in the wrong place or phrasing the question suboptimally, but here is my best shot:

How to go about determining the correct relative dimensions of a non-regular icosahedron that, should it be used to cast a physical die, the probability distribution would be:

[IMG]http://www.engineersedge.com/engineering-forum/attachment.php?attachmentid=1599&stc=1[/IMG]

If it helps to have a fixed dimension to work with, assume a 20mm vertex-to-vertex diameter.