Reuleux Triangle

ps = {p1, p2,
    p3} = {{Sqrt[3]/4, 0}, {-Sqrt[3]/4, -0.5}, {-Sqrt[3]/4, 0.5}};
min[\[Theta]_] := Piecewise[{
    {Norm[ps[[1]]], -Pi/3 < \[Theta] < Pi/3}
    },
   0
   ];
graphics[\[Theta]_] := ({
    {
     FaceForm[Directive[Opacity[0.33], RGBColor[0.5, 0.7, 0.8]]],
     EdgeForm[Black],
     Disk[#, 1] & /@ ps
     },
    Point[Mean[ps]],
    PointSize[Large],
    Darker@Red,
    Thickness[0.003],
    Piecewise[
     {{
       {
        Point[p1],
        Line[{p1 - 10 {Sin[\[Theta]], Cos[\[Theta]]},
          p1 + 10 {Sin[\[Theta]], Cos[\[Theta]]}}],
        Line[{p1 -
           10 {Sin[\[Theta]],
             Cos[\[Theta]]} - {Cos[\[Theta]], -Sin[\[Theta]]},
          p1 + 10 {Sin[\[Theta]],
             Cos[\[Theta]]} - {Cos[\[Theta]], -Sin[\[Theta]]}}],
        RGBColor[0, 0.3, 0.4],
        Line[{
          p1,
          p1 - {Cos[\[Theta]], -Sin[\[Theta]]}
          }]
        }
       ,
       -Pi/6 <= \[Theta] < Pi/6
       },

      {
       With[{\[Phi] = \[Theta] + Pi},
        {
         Point[p3],
         Line[{p3 - 10 {Sin[\[Phi]], Cos[\[Phi]]},
           p3 + 10 {Sin[\[Phi]], Cos[\[Phi]]}}],
         Line[{p3 -
            10 {Sin[\[Phi]],
              Cos[\[Phi]]} - {Cos[\[Phi]], -Sin[\[Phi]]},
           p3 + 10 {Sin[\[Phi]],
              Cos[\[Phi]]} - {Cos[\[Phi]], -Sin[\[Phi]]}}],
         RGBColor[0, 0.3, 0.4],
         Line[{
           p3,
           p3 - {Cos[\[Phi]], -Sin[\[Phi]]}
           }]
         }
        ]
       ,
       Pi/6 <= \[Theta] <=  Pi/2
       }
      },
     {}
     ]
    });
Manipulate[
 Graphics[
  Rotate[
   graphics[\[Theta]],
   \[Theta] - Pi/2,
   Mean[ps]
   ]
  , PlotRange -> 2, ImageSize -> 500],
 {\[Theta], -Pi/6, Pi/2}]