```Date: Nov 18, 2012 4:02 AM
Author: Roger Bagula
Subject: 3d model failure with Cylinders

I don't get a 3d model out of this for some reason:only the rim torus outputs as a 3d model.Clear[n, m, gw, g2, R]n = 7; m = 3; dt = 2 Pi/n; dtm = 2 Pi/m; r =  1.0/(1 - Sin[dt/2]/Cos[dtm/2]); R = r Cos[(dt + dtm)/2]/Cos[dtm/2];ToMatrix[z_,    r_] := (I/r) {{z, r^2 - z Conjugate[z]}, {1, -Conjugate[z]}};alist := Table[  ToMatrix[r Exp[I t], r - 1], {t, dt/2, 2 Pi, dt}]; Tlist :=  Join[{IdentityMatrix[2]}, alist];homography[{{a_, b_}, {c_, d_}}, z_] := (a z + b)/(c z + d);FindT[T0_, Tlist_] :=   MemberQ[Tlist,    T_ /; Abs[homography[T, 0] - homography[T0, 0]] < 1.0*^-3];i2 = 1; Do[i1 = i2 + 1; i2 = Length[Tlist];  Do[Scan[(T = Tlist[[i]].#;      If[! FindT[T, Tlist], Tlist = Append[Tlist, T]]) &, alist], {i,    i1, i2}], {3}];R0 = {{Cos[2*Pi/n], Sin[2*Pi/n], 0}, {-Sin[2*Pi/n], Cos[2*Pi/n],     0}, {0, 0, 1}};Clear[g2, g3, g4]g2 = ParametricPlot3D[{(37 + Cos[\[Alpha]])*Cos[\[Beta]],                                         (37 + Cos[\[Alpha]])*       Sin[\[Beta]] ,                                                 Sin[\[Alpha]] }/     10 + {0, 0, (6.5/2)*R},                                         {\[Alpha], 0,     2*\[Pi]}, {\[Beta], 0, 2*\[Pi]}, Boxed -> False, Axes -> False,    PlotRange -> All, ColorFunction -> "Pastel",    MeshFunctions -> {#1 &}];g3 = Graphics3D[{ColorData["LightTemperatureMap"][0.75],    Table[Map[     Cylinder[       Table[z = homography[#, R Exp[I t]];         MatrixPower[R0, l].{Re[z], Im[z], Abs[z]}, {t, 0, 2 Pi, dt}],        1/(10 + Abs[z])] &, Tlist], {l, 0, 7}]}, Boxed -> False]g4 = Graphics3D[{ColorData["LightTemperatureMap"][0.75],    Table[Map[     Cylinder[       Table[z = homography[#, R Exp[I t]];         MatrixPower[R0, l].{Re[z], Im[z], 6.5*R - Abs[z]}, {t, 0,          2 Pi, dt}], 1/(10 + Abs[z])] &, Tlist], {l, 0, 7}]},   Boxed -> False]gw = Show[{g2, g3, g4}, Boxed -> False, ImageSize -> 1000,   ViewPoint -> {5, 5, 5}]Export["hyperbolic8_cage.3ds", gw]Export["hyperbolic8_cage.obj", gw]Export["hyperbolic8_cage.stl", gw]I expected a cage type 3d model.I've also had large triangle output in cylinders as 3d modelsthat have to be removed.
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