Please help me find a good picture of this geometric figure

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
If you want others then you should look up the link for archimedian solids. There are 13 of them.