or better still, a way of generating one of these at will. The “ten great circles forming a pattern of stars” figure. The only example I could Google to even show what I’m talking about is HERE ,(figure III), but I’d really like a better one.
Looks to me like you might want an icosidodecahedron
http://mathworld.wolfram.com/Icosidodecahedron.html
If you want others then you should look up the link for archimedian solids. There are 13 of them.