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How can I plot two parts of Möbius strip bonding together like the following picture?enter image description here

The parametric equations:

x[u_, v_] := (2 + v Sin[u/2]) Cos[u]
y[u_, v_] := (2 + v Sin[u/2]) Sin[u]
z[u_, v_] := v Cos[u/2]

I take the plots

m1 = ParametricPlot3D[{x[u, v], y[u, v], z[u, v]}, {u, \[Pi]/3, 
   5 \[Pi]/3 }, {v, -1/2, 1/2}, Boxed -> False, 
   PlotPoints -> {150, 150}, Mesh -> None, PlotStyle -> Opacity[.5], 
   PlotStyle -> LightBlue]
m2 = ParametricPlot3D[{x[u, v], y[u, v], z[u, v]}, {u, 4 \[Pi]/3, 
    8 \[Pi]/3 }, {v, -1/2, 1/2}, Boxed -> False, 
  PlotPoints -> {150, 150}, Mesh -> None, PlotStyle -> Opacity[.5], 
   PlotStyle -> Red]

 Show [m1, m2]

I tried this one, but I can't get it to work.

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Sticking as close as possible to what you wrote:

x[u_, v_] = (2 + v Sin[u/2]) Cos[u];
y[u_, v_] = (2 + v Sin[u/2]) Sin[u];
z[u_, v_] = v Cos[u/2];

m1 = ParametricPlot3D[{x[u, v], y[u, v], z[u, v]}, {u, π/3, 5π/3}, {v, -1/2, 1/2},
  Boxed -> False, PlotPoints -> {150, 150}, Mesh -> None,
  PlotStyle -> {LightBlue, Opacity[.5]}]

m2 = ParametricPlot3D[{x[u, v], y[u, v], z[u, v]}, {u, 4π/3, 8π/3}, {v, -1/2, 1/2},
  Boxed -> False, PlotPoints -> {150, 150}, Mesh -> None,
  PlotStyle -> {Red, Opacity[.5]}]

Show[m1, m2, PlotRange -> All]

enter image description here

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  • $\begingroup$ PlotRange -> All That just is my need ! Thanks ! $\endgroup$ – user553010 Mar 9 at 8:53
  • $\begingroup$ The other thing I changed was the two separate PlotStyle commands that need to be merged into one. $\endgroup$ – Roman Mar 9 at 9:29
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moebiusstrip[a_][u_, v_] := {a Cos[u] + v Cos[u/2] Cos[u], 
     a Sin[u] + v Cos[u/2] Sin[u], v Sin[u/2]}

mss := moebiusstrip[2]

a := .6
z1 = ParametricPlot3D[mss[u, v], {u, 0, 2 π}, {v, -a, a},
     PlotPoints -> {24, 8}]

enter image description here

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  • $\begingroup$ Not the Möbius strip itself ,but the two distinct parts of Möbius strip bonding together (In my post's picture , left part of Möbius strip and right part of Möbius strip bound together overlapping A and B, and then the bouned two parts make up the whole Möbius strip ).Thanks all the same. $\endgroup$ – user553010 Mar 9 at 8:39

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