Yeah, I know, it's not really an icosahedral tube.
Some of these names get really difficult, and long, and annoying.
But she looks simple and elegant, doesn't she? (she?)
So, anyway, I started with a truncated icosahedron, extruded the pentagonal faces, added handles, blah-de-blah, etc., etc.
And it ends up being more of a tubular dodecahedron, with curved edges.
5.028 w x
4.388 d x
1.98 w x
1.728 d x