Trefoil Torus Knot

by Stewart Dickson
Mathematica code

     r1 = 1.0

     r2 = 3.0

     Bx [u_, v_] := (r2 + r1 * Cos[u/2.0]) * Cos[u/3.0]
     By [u_, v_] := (r2 + r1 * Cos[u/2.0]) * Sin[u/3.0]
     Bz [u_, v_] := r1 * Sin[u/2.0]

     x [u_, v_] := N[Bx [u, v]] + r1 * Cos[u/3.0] * Cos[v - Pi]
     y [u_, v_] := N[By [u, v]] + r1 * Sin[u/3.0] * Cos[v - Pi]
     z [u_, v_] := N[Bz [u, v]] + r1 * Sin[v - Pi]

     ParametricPlot3D[N[{x[u, v], y[u, v], z[u, v]}],
  	 {u, 0, 12 Pi}, {v, 0, 2 Pi}, PlotPoints -> {144, 12}]

Texture mapped VRML object: