I made a few of the simpler models, but never got much further than the dodecahedron. I certainly never got as far as making any of the fiddly stellated ones.
So today, when I came across a posting in Google+ about Anselm Levskaya's website polyHédronisme, I was taken right back to those days. Playing with this interactive web-based systems is much easier than fiddling with card, glue, and scissors, though. Type in a few commands, and a zoomable, rotatable polyhedron appears!
I've spent my afternoon playing around on this site, and reading up on Conway polyhedron notation that is used to define shapes, and now I can say I have at last "made" some of these polyhedra.
polyHédronisme that achieves this is \(k(5,1.41)D\), which means: start with a dodecahedron \(D\), then raise a pyramid of height \(1.41\) on each \(5\)-sided face.
polyHédronisme that achieves this is \(k(3,-0.36)I\), which means: start with an icosahedron \(I\), then indent a pyramid of height \(0.36\) on each \(3\)-sided face.
polyHédronisme that achieves this is \(k(3,1.51)I\), which means: start with an icosahedron \(I\), then raise a pyramid of height \(1.51\) on each \(3\)-sided face.
So much for standard polyhedra. But polyHédronisme doesn't stop there. I had great fun playing about with the notation language, producing weird and wonderful forms:
|(i) \(k(20,1)bk(3,2)I\) (ii) \(k(12,1)k(10,2)bk(5,1)D\) (iii) \(k(20,-0.3)k(6,0.3)bk(3,-0.3)I\)|
The results of play can only really be appreciated on the site itself, rotating the polyhedra, and getting a real feel for their shapes, with all their dips and bumps. A marvellous site.
* The book Polyhedron Models has helpful stellation diagrams that allow these heights to be calculated, with a little trigonometry.