# Return to Answer

 4 added 86 characters in body edited Nov 22 '17 at 2:15 David G. Stork 26.2k22 gold badges2323 silver badges5959 bronze badges torus = ParametricPlot3D[ {Cos[θ] (1 + .3 Cos[φ]), Sin[θ] (1 + .3 Cos[φ]), .3 Sin[φ]}, {θ, 0, 2 π}, {φ, 0, 2 π}, PlotStyle -> Opacity[0.3]]; line = ParametricPlot3D[ {Cos[.2 + t (.8 - .2)] (1 + .3 Cos[.1 + t (2.5 - .1)]), Sin[.2 + t (.8 - .2)] (1 + .3 Cos[.1 + t (2.5 - .1)]), .3 Sin[.1 + t (2.5 - .1)]}, {t, 0, 1}, PlotStyle -> Directive[Thick, Red]]; Show[torus, line, Boxed->False, Axes -> None]  Now just insert your six points and draw the lines between each pair by this method. torus = ParametricPlot3D[ {Cos[θ] (1 + .3 Cos[φ]), Sin[θ] (1 + .3 Cos[φ]), .3 Sin[φ]}, {θ, 0, 2 π}, {φ, 0, 2 π}, PlotStyle -> Opacity[0.3]]; line = ParametricPlot3D[ {Cos[.2 + t (.8 - .2)] (1 + .3 Cos[.1 + t (2.5 - .1)]), Sin[.2 + t (.8 - .2)] (1 + .3 Cos[.1 + t (2.5 - .1)]), .3 Sin[.1 + t (2.5 - .1)]}, {t, 0, 1}, PlotStyle -> Directive[Thick, Red]]; Show[torus, line, Boxed->False, Axes -> None]  torus = ParametricPlot3D[ {Cos[θ] (1 + .3 Cos[φ]), Sin[θ] (1 + .3 Cos[φ]), .3 Sin[φ]}, {θ, 0, 2 π}, {φ, 0, 2 π}, PlotStyle -> Opacity[0.3]]; line = ParametricPlot3D[ {Cos[.2 + t (.8 - .2)] (1 + .3 Cos[.1 + t (2.5 - .1)]), Sin[.2 + t (.8 - .2)] (1 + .3 Cos[.1 + t (2.5 - .1)]), .3 Sin[.1 + t (2.5 - .1)]}, {t, 0, 1}, PlotStyle -> Directive[Thick, Red]]; Show[torus, line, Boxed->False, Axes -> None]  Now just insert your six points and draw the lines between each pair by this method. 3 edited body edited Nov 22 '17 at 1:17 David G. Stork 26.2k22 gold badges2323 silver badges5959 bronze badges torus = ParametricPlot3D[ {Cos[θ] (1 + .3 Cos[φ]), Sin[θ] (1 + .3 Cos[φ]), .3 Sin[φ]}, {θ, 0, 2 π}, {φ, 0, 2 π}, PlotStyle -> Opacity[0.3]]; line = ParametricPlot3D[ {Cos[.2 + t (.8 - .2)] (1 + .3 Cos[.1 + t (12.5 - .1)]), Sin[.2 + t (.8 - .2)] (1 + .3 Cos[.1 + t (12.5 - .1)]), .3 Sin[.1 + t (12.5 - .1)]}, {t, 0, 1}, PlotStyle -> Directive[Thick, Red]]; Show[torus, line, Boxed->False, Axes -> None]  torus = ParametricPlot3D[ {Cos[θ] (1 + .3 Cos[φ]), Sin[θ] (1 + .3 Cos[φ]), .3 Sin[φ]}, {θ, 0, 2 π}, {φ, 0, 2 π}, PlotStyle -> Opacity[0.3]]; line = ParametricPlot3D[ {Cos[.2 + t (.8 - .2)] (1 + .3 Cos[.1 + t (1.5 - .1)]), Sin[.2 + t (.8 - .2)] (1 + .3 Cos[.1 + t (1.5 - .1)]), .3 Sin[.1 + t (1.5 - .1)]}, {t, 0, 1}, PlotStyle -> Directive[Thick, Red]]; Show[torus, line, Boxed->False, Axes -> None]  torus = ParametricPlot3D[ {Cos[θ] (1 + .3 Cos[φ]), Sin[θ] (1 + .3 Cos[φ]), .3 Sin[φ]}, {θ, 0, 2 π}, {φ, 0, 2 π}, PlotStyle -> Opacity[0.3]]; line = ParametricPlot3D[ {Cos[.2 + t (.8 - .2)] (1 + .3 Cos[.1 + t (2.5 - .1)]), Sin[.2 + t (.8 - .2)] (1 + .3 Cos[.1 + t (2.5 - .1)]), .3 Sin[.1 + t (2.5 - .1)]}, {t, 0, 1}, PlotStyle -> Directive[Thick, Red]]; Show[torus, line, Boxed->False, Axes -> None]  2 added 5 characters in body edited Nov 22 '17 at 0:47 David G. Stork 26.2k22 gold badges2323 silver badges5959 bronze badges torus = ParametricPlot3D[ {Cos[θ] (1 + .3 Cos[φ]), Sin[θ] (1 + .3 Cos[φ]), .3 Sin[φ]}, {θ, 0, 2 π}, {φ, 0, 2 π}, PlotStyle -> Opacity[0.3]]; line = ParametricPlot3D[ {Cos[.2 + t (.8 - .2)] (1 + .3 Cos[.1 + t (1.95 - .1)]), Sin[.2 + t (.8 - .2)] (1 + .3 Cos[.1 + t (1.95 - .1)]), .3 Sin[.1 + t (1.95 - .1)]}, {t, 0, 1}, PlotStyle -> Directive[Thick, Red]]; Show[torus, line]line, Boxed->False, Axes -> None]  torus = ParametricPlot3D[ {Cos[θ] (1 + .3 Cos[φ]), Sin[θ] (1 + .3 Cos[φ]), .3 Sin[φ]}, {θ, 0, 2 π}, {φ, 0, 2 π}, PlotStyle -> Opacity[0.3]]; line = ParametricPlot3D[ {Cos[.2 + t (.8 - .2)] (1 + .3 Cos[.1 + t (.9 - .1)]), Sin[.2 + t (.8 - .2)] (1 + .3 Cos[.1 + t (.9 - .1)]), .3 Sin[.1 + t (.9 - .1)]}, {t, 0, 1}, PlotStyle -> Directive[Thick, Red]]; Show[torus, line]  torus = ParametricPlot3D[ {Cos[θ] (1 + .3 Cos[φ]), Sin[θ] (1 + .3 Cos[φ]), .3 Sin[φ]}, {θ, 0, 2 π}, {φ, 0, 2 π}, PlotStyle -> Opacity[0.3]]; line = ParametricPlot3D[ {Cos[.2 + t (.8 - .2)] (1 + .3 Cos[.1 + t (1.5 - .1)]), Sin[.2 + t (.8 - .2)] (1 + .3 Cos[.1 + t (1.5 - .1)]), .3 Sin[.1 + t (1.5 - .1)]}, {t, 0, 1}, PlotStyle -> Directive[Thick, Red]]; Show[torus, line, Boxed->False, Axes -> None]  1 answered Nov 22 '17 at 0:33 David G. Stork 26.2k22 gold badges2323 silver badges5959 bronze badges