Hopf Fibration, 12.7 cm

A larger model of the Hopf fibration with 2 mm  diameter wires; 12.7 cm across, large enough to print in the steels. 

The easiest way to understand this model of the Hopf fibration (actually 2 of them, crossing one another at right angles) may be to see it as a torus surface being turned inside-out through a hole in its side. The structure is entirely composed of circles, or arcs of them, forming a deformed grid on the torus. 

For a great video of the Hopf fibration, see: http://nilesjohnson.net/hopf.html

For a clear discussion of the math, and of the 4th dimension and stereographic projection, with great videos, see:  http://www.dimensions-math.org/Dim_regarder_E.htm