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r[t_] := {Sin[t] + 2 Sin[2*t], Cos[t] - 2 Cos[2*t], -Sin[3*t]};
T[t_] := 1/Norm[r'[t]]*r'[t];
U[t_] := 1/Norm[r''[t]]*r''[t];
V[t_] := Cross[T[t], U[t]];

W[a_, d_, t_] := r[t] + d*Cos[a]*U[t] + d*Sin[a]*V[t]

Manipulate[With[{d = .5, M = 124, Q = 124},
 Graphics3D[
  Table[
    GraphicsComplex[
     Flatten[Table[
      W[(a + s)*2 Pi/3, d, t + s*8*Pi/M],
     {t, {j*2 Pi/M, (j + 1) 2 Pi/M}}, {a, 0, 2, 1}], 1],
      Polygon[{{1, 2, 5, 4}, {2, 3, 6, 5}, {3, 1, 4, 6}}]],
  {j, 0, Q, 1}],
 Lighting -> "Neutral", Boxed -> False, ViewPoint -> Above, 
 ImageSize -> 600, PlotRange -> 3.5]],
{s, 0, 1}]


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