recreating a mathematical 3D shape

Hello, I am trying to recreate a shape shown in the attached photo, from the attached article I have tried to create this shape in MATLAB as shown in the code bellow , from this formula i get a 2D shape and not the shown 3D shape , how to create this 3D shape? Thanks

theta_0=15; alpha=60; delta=90; r0=2.3; D=15.2; a=sin(theta_0)/(tan(alpha)); r1=r0*exp(a*phi); r1=r0*exp(a*phi-pi);