Knots can also be identified with spaces that don't seem "knotty" at first glance.

See Thurston's Knots to Narnia[1] and Not Knot[2]. PolyCut[3] is a little applet that can visualize these knotty portals.

[1] https://www.youtube.com/watch?v=IKSrBt2kFD4 [2] https://www.youtube.com/watch?v=zd_HGjH7QZo [3] http://facstaff.susqu.edu/brakke/polycut/polycut.htm