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Are there topological spaces with non trivial homotopy groups $\pi_{>=2}$ that are visualizeable?

I'm thinking about the the shape of what is called a "higher dimensional hole" but I can't find anything about it...

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 On the face of it, this would seem a better fit at maths.stackexchange.com. – Andrew Stacey Oct 14 2011 at 9:09
I agree with Andrew and also voted to close. However, you might enjoy thinking about the geometry of the Hopf fibration. Look it up on Wikipedia. – Dan Petersen Oct 14 2011 at 9:13
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 en.wikipedia.org/wiki/… is probably the first page you want to look at. – Marco Golla Oct 14 2011 at 9:21
Niles Johnson has an animation of the Hopf fibration on his website that might be helpful. – Sean Tilson Oct 14 2011 at 15:34

closed as off topic by Andrew Stacey, Dan Petersen, Mark Grant, David Roberts, Igor Rivin Oct 14 2011 at 10:11

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