I'm not on this site as much as I used to be, but I have received quite a few "you've got a new PM on cake central" and its pretty much always asking how I did my 20 sided die. A recent one got me thinking I should just make a post so people don't have to email. Though please feel free to PM if you have any questions. CC will let me know you rang.
So first off, a 20 sided die seems really complicated. But we really took a look at it, and found a way to break it down easier.
We found the wiki article for "icosahedron" to be a big help. There is an orange & yellow flat template that may be of use, as well as some formulas if that's your thing. But the big breakthrough was the interactive rotating model. From that we broke the cake down like this.
We chose to balance the cake on one point for ease of carving & layout. This makes basic shape a pentagon. You'll need two of the same size pentagon boards. These pentagons DO NOT line up - each point will meet the middle of one of the sides. 10 equal triangles form the middle of the die - 5 point up & 5 point down. I wish I could give you a size or template, but its all dependent on your size cake - but DO make a template of your triangle face! (or two!) Each of the bases of these triangles form the pentagons. 5 more triangles share the other side of that pentagon, with their points coming together to make the top & bottom points. (Think of a crown shape, then push in the tops to meet.)
So you'll need to figure out what to make your base out of. . . we used styrofoam. I know, I know...use whatever makes you happy. Doing this again, we would either make a special base of wood or make a pentagon "table" and use RKT under it for the point. But the main point is the cake isn't actually resting on this point, of course. We had a support running through the middle of the cake that screwed into the base. 3 more dowels kept the base on point, and those were hidden by the smaller die. Again, I would do it different now, but that's what we did then. You can see one of the side support dowels in the pic.
On top of this base, you'll use round cakes, larger than you need. The edges of these triangles point OUT - the top or bottom-most points will be the highest, the triangles will go lower into the base at the pentagon. It really helps to have a die to look at. Put the second pentagon on top of the cake & use your triangle templates to help know where to carve. Use a very very dense cake & keep your edges as sharp as possible. Then repeat the bottom for the top point.
We coated the entire cake in a thick layer of buttercream and a large sheet of fondant and from there I used my fingers to mold & sharpen the edges of the die. (Like Bronwen Weber molds her fondant on her cakes -- see her face in the pumpkin cake for the food network challenge.) You have to work quickly, just pinch the edges up gently. Once the fondant starts setting they'll stay.
The numbers in a 20 sided die don't all go the same way. Use a real one for reference. We just painted our numbers on, but cutting them out of fondant would look much better.
So good luck & hope this helps!
The cake: http://cakecentral.com/gallery/2010505