Study of the Pentakis Icosidodecahedron

thingiverse

I've been in kind of a mood for domes lately and after one of my last projects which involved a lot of trigonometry I thought I'd try to tackle something a little more complex and went with the 80-sided Pentakis Icosidodecahedron. It's a pretty familiar polyhedron that kind of looks like playground equipment or some kind of omnidirectional radar/sigint receiver or a mini "Spaceship Earth" at EPCOT Center. This is a parametric design so it is somewhat customizeable. Since the Pentakis Icosidodecahedron is based on the Icosidodecahedron I've include a few examples of those as well and the ability to generate them with the customizer script which I wrote in OpenSCAD. All example .STL files that I have generated have a maximum dimension of two imperial inches or 50.8mm. The only thing I know for sure about this polyhedron is that the isosceles triangles make the shallow pentagonal pyramids with sides measuring 0.54653 (times the dome) radius and the equilateral triangles padding the pentagons have sides measuring 0.61803 (times the dome radius). I'm honestly not even sure what the dihedral angle is--assuming there's only one ... but I'll edit this post if I find out.