Another way to tackle this is to download 3D mesh files of actual viruses. Here is a page with many such files. First you grab the links to STL files:
virusLinks =
Import["https://www.rbvi.ucsf.edu/Outreach/technotes/ModelGallery/index.html",
"Hyperlinks"] // Select[StringEndsQ@".stl"]
(*
{https://www.rbvi.ucsf.edu/Outreach/technotes/ModelGallery/4.5S.stl,
https://www.rbvi.ucsf.edu/Outreach/technotes/ModelGallery/FfhM3.stl,
https://www.rbvi.ucsf.edu/Outreach/technotes/ModelGallery/single-3fold-ring.stl,
https://www.rbvi.ucsf.edu/Outreach/technotes/ModelGallery/single-3fold.stl,
https://www.rbvi.ucsf.edu/Outreach/technotes/ModelGallery/STL/clathrin.stl,
https://www.rbvi.ucsf.edu/Outreach/technotes/ModelGallery/STL/dengue_8A_IAU_1p58.stl,
https://www.rbvi.ucsf.edu/Outreach/technotes/ModelGallery/STL/FMDV_5A.stl,
https://www.rbvi.ucsf.edu/Outreach/technotes/ModelGallery/STL/hepB.stl,
https://www.rbvi.ucsf.edu/Outreach/technotes/ModelGallery/STL/MurinePolyoma.stl,
https://www.rbvi.ucsf.edu/Outreach/technotes/ModelGallery/STL/HRV1-4A-02-3-4.stl,
https://www.rbvi.ucsf.edu/Outreach/technotes/ModelGallery/STL/rotavirus-6A.stl,
https://www.rbvi.ucsf.edu/Outreach/technotes/ModelGallery/STL/noda_4A.stl,
https://www.rbvi.ucsf.edu/Outreach/technotes/ModelGallery/STL/ParvoB19_5A.stl,
https://www.rbvi.ucsf.edu/Outreach/technotes/ModelGallery/STL/4tna_15_80.stl}*)
Now you can import these as Graphics3D
objects. Here is the parvovirus B19:
Normal@Import[virusLinks[[-2]], {"STL", "Graphics3D"}]

and here's a hack method method suggested by J.M. to plot the imported GraphicsComplex
with a custom color function
plotvirus[link_] :=
With[{virus = Import[link, {"STL", "GraphicsComplex"}]},
Graphics3D[
Append[ MapAt[Insert[#, EdgeForm[], 1] &, virus, {2}],
VertexColors -> (ColorData[
"GreenPinkTones"] /@ (Rescale[
Norm /@ Standardize[First[virus], Mean, 1 &]]))],
Boxed -> False]]
For some reason I like the green-pink tones. Here is a plot of the murine polyomavirus

These plots will really slow down your computer (at least they do for me), since they have hundreds of thousands of vertices. I had to rasterize them in order to create this image:
