The gyroelongated pentagonal rotunda is one of the Johnson solids, or so Wikipedia tells me. So why print one? Well, I don't actually plan to as such, but inspired by the possibilities of many other domes that people have designed, I might get round to making one of my own. But why the oddly-named solid, rather than one of the more standard dome designs? The advantage of the Johnson solids (along with their Archimedean and Platonic cousins) is that they can be made with rods that are all exactly the same length. My vision is of turning up somewhere with just a bag of plastic connectors, and then fabricating the rods out of anything that comes to hand (say, sheets of a newspaper rolled up into cylinders) - and hey presto, a huge dome! Well, so goes the theory; as yet I have done nothing other than make a 3D model of what the completed dome might look like.
Perhaps of the most interesting aspect is the way the models were generated: I used OpenSCAD, but the scripts were generated by a Python script. I'm certainly not the first to do that, but as part of creating it I came up with some utility functions there that allow positioning of a cylinder, or arbitrarily-shaped flat polygon, by co-ordinates: rather than having to figure out the rotate()/translate() to put your cylinder in a particular location, just pass the co-ordinates of the two endpoints (the centres thereof), and the function will do the rest (and similarly for the polygons). These might come in handy for those situations where you know exactly where you want something to go, but don't want to figure out the precise translation/rotation to get it there.