I hvae just skimmed (literally - no words went in except Buckminsterfullerene). The ones near the top are interestingly irregular, the ones at the bottom look familiar and I WANT THAT DRAWING SOFTWARE!!

*cough* sorry.

It's all there to be downloaded, for your comfort and convenience :-) Not much of a user interface, though, I grant you.

Actually I think the bit I'm most proud of is the code which takes an arbitrary polyhedron description and produces a correctly formed net with all the tabs in the right places and everything, without requiring any intelligent input about the layout. That was hard.

really? i would have thought that you could just tell the computer to effectivly do what you were saying about cutting it out and sticking it together with the faces in the places there numbers are. Shows what I know (to me that sounds like an easy thing to make a computer do, because I know how to do it). Also, the tabs just go on every other outer edge, until you get into the very beautiful, often spiky, and impossible to construct world of non-convex polyhedra.

The tabs almost go on every other edge, but not quite; the special case is that you want there to be at least one face with no tabs on at all, because that makes life easier on the very last face you stick down. So instead of that reasonably simple policy, I had to actually keep track of which edges of the net were going to end up coming together when it was folded back up, and use a general mechanism to ensure that exactly one of each such pair of edges acquired a tab.

The really hard bit, though, was deciding on the shapes of the tabs. For a start you need to know the shape of the face the tab will stick on to (no point making it an almost-rectangular trapezium if it's going to stick on to an equilateral triangle), and then you need to shorten the tab if it threatens to collide with other faces in the laid-out net, and finally you need to arrange that no two tabs themselves collide with each other. At first I thought that was going to be an AI-complete problem, but as it turned out there are ways to do it...

ah, yes when making it on paper it's easy to just faff with them to get the most sensible shape and size. However, in my personal experience it makes for more stable hedrons to have the last face with some tabs on - it also makes it easier to stick because you can poke them down and they hold it in place without you having to sit there holding it in place ;). Of course, I've been using construction paper, and not card. That might make a difference.