For the coordinates X[t], Y[t] of a
given point we have
X[t]=a*cos(t)+(1-a)*cos(3*t);
Y[t]=(a)*sin(t)-(1-a)*sin(3*t);
1-X[t]^2-Y[t]^2=16*a*cos(t)
^2*(sin(t)^2)*(1-a)=FULL SQUARE!=>
If Z[t]=4*cos(t)*sin(t)*(a*(1-a))^(1/2), then
X[t]^2+Y[t]^2+Z[t]^2=1(i.e., lies on the unit SPHERE!!!).
For some reason, which will be published elsewhere(Sic!),The Optimal Value for the parametr a is a=0.6339, as will be
shown elsewhere. Let us call it "THE YIN-YANG PLATINUM SECTION"
And we shall always put a=(1/2)(3-3^(1/2))=0.6339
;Below is given this ParametricPlot3D of such a 3D-ASTROID
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