Is this (self intersecting) surface considered one sided?

Question

I wanted to apply stokes theorem on a curve (in black) that possibly looks like the seam of a tennis ball. I make a surface by drawing a line from the origin to each point of this curve.

I get a surface like this and wanted to know if it's actually one sided or not - since I wasn't sure how you can cross the intersection bits, whether you carry on as you would expect - or you move from one part to the other on the intersection instead of crossing the edge (black curve).

The reason why I am using a surface like this is because I can explicitly define the normal along it for my problem.

(mathematica code):

tennisballseam[n_, a_, b_, c_][t_] := {-a*(Cos[t]*(b^2 + c^2*n^2*Cos[n*t]^2) + 
  c^2*n^3*Sin[t]*Sin[2*n*t]/2)/(Sqrt[
   b^2*Cos[t]^2 + c^2*n^2*Cos[n*t]^2 + a^2*Sin[t]^2]*
  Sqrt[a^2*b^2*Cos[t]^4 + b^2*c^2*n^2*Cos[n*t]^2*Sin[t]^2 + 
    a^2*b^2*Sin[t]^4 + a^2*c^2*n^4*Sin[t]^2*Sin[n*t]^2 + 
    Cos[t]^2*(a^2*c^2*n^2*Cos[n*t]^2 + 
       b^2*(2*a^2*Sin[t]^2 + c^2*n^4*Sin[n*t]^2)) + 
    a^2*c^2*n^3*Sin[2*t]*Sin[2*n*t]/2 - 
    b^2*c^2*n^3*Sin[2*t]*Sin[2*n*t]/2]),b*(-2*(a^2 + c^2*n^2*Cos[n*t]^2)*Sin[t] + 
  c^2*n^3*Cos[t]*Sin[2*n*t])/(2*
  Sqrt[b^2*Cos[t]^2 + c^2*n^2*Cos[n*t]^2 + a^2*Sin[t]^2]*
  Sqrt[a^2*b^2*Cos[t]^4 + b^2*c^2*n^2*Cos[n*t]^2*Sin[t]^2 + 
    a^2*b^2*Sin[t]^4 + a^2*c^2*n^4*Sin[t]^2*Sin[n*t]^2 + 
    Cos[t]^2*(a^2*c^2*n^2*Cos[n*t]^2 + 
       b^2*(2*a^2*Sin[t]^2 + c^2*n^4*Sin[n*t]^2)) + 
    a^2*c^2*n^3*Sin[2*t]*Sin[2*n*t]/2 - 
    b^2*c^2*n^3*Sin[2*t]*Sin[2*n*t]/2]), -c*n*((a^2 - b^2)*Cos[t]*Cos[n*t]*Sin[t] + b^2*n*Cos[t]^2*Sin[n*t] + 
  a^2*n*Sin[t]^2*Sin[n*t])/(Sqrt[
   b^2*Cos[t]^2 + c^2*n^2*Cos[n*t]^2 + a^2*Sin[t]^2]*
  Sqrt[a^2*b^2*Cos[t]^4 + b^2*c^2*n^2*Cos[n*t]^2*Sin[t]^2 + 
    a^2*b^2*Sin[t]^4 + a^2*c^2*n^4*Sin[t]^2*Sin[n*t]^2 + 
    Cos[t]^2*(a^2*c^2*n^2*Cos[n*t]^2 + 
       b^2*(2*a^2*Sin[t]^2 + c^2*n^4*Sin[n*t]^2)) + 
    a^2*c^2*n^3*Sin[2*t]*Sin[2*n*t]/2 - 
    b^2*c^2*n^3*Sin[2*t]*Sin[2*n*t]/2])};

ParametricPlot3D[{(tennisballseam[2, 2.8, 2.8, 1][t] + 
 2) z, (tennisballseam[2, 2.8, 2.8, 1][t] + 2)}, {z, 0, 1}, {t, 0,6 \[Pi]}, PlotPoints -> 20, PlotRange -> {0, 3}, PlotStyle -> {Automatic, Red, Thick}]