graphics3d - 3D surface that looks like a virus

I have been recently using Mathematica for composing animations that are part of the supplementary information of my papers.

I am currently trying to build an animation that involves a viral particle. I am having problem representing a viral particle.

Does anyone know a 3D surface that looks like virus? I found a reasonable candidate from this.

Here is the code:

State = {0, Sqrt[7], 0, 0, 0, 0, -Sqrt[11], 0, 0, 0, 0, -Sqrt[7], 0};
nState = State/Norm[State]; Lam = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
For[i = 1, i < 14, i++,
 Lam[[i]] = 
  Sqrt[Binomial[12, i - 1]]*(Cos[theta/2]^(13 - i))*E^(I*phi*(i - 1))*(Sin[theta/2]^(i - 1))]
sproduct = Norm[nState.Lam];

SphericalPlot3D[(sproduct^2) + 0.005, theta, phi, PlotPoints -> {50, 50}, Boxed -> False]

The problem is, the virus that I try to animate is more globular than the plot above; so I prefer to use different 3D plot. Does anyone know any other 3D surface that looks like a viral particle?

This is the picture of the viral particle that I desire

Thank you.