SetDirectory["C:\\drorbn\\AcademicPensieve\\2015-01"];

R=((Sqrt[2])/2)RotationMatrix[{{0,1,0,1},{0,0,0,1}}];
λ[w_,x_,y_,z_] := (({w,x,y})/(1-z));
MakeImage["Order4Torus",
ParametricPlot3D[
λ@@(R.{Cos[t],Sin[t],Cos[s],Sin[s]}),
{t,0,2π}, {s,0,2π},
RegionFunction -> ((((#4-(π/2)))^2)+(((#5-(π/2)))^2)>(0.4^2) &),
Boxed -> False, Axes -> False, PlotRange -> All, PlotPoints -> 20, MaxRecursion -> 5,
ViewPoint->{1.84837,1.96957,-2.03821},ViewVertical->{0.0295198,6.86933,0.179905}
], ImageSize -> 720
]

Competition:
http://www.math.union.edu/~dpvc/math/4d/stereo-projection/welcome.html,
http://www.math.union.edu/~dpvc/tfb/icms-poster/torus/welcome.html,
http://commons.wikimedia.org/wiki/File:Inside-out_torus _ %28 animated,_small %29.gif.