This is what you get if you stellate an icosahedron seventeen times. The eighteenth stellation “loops” back around to the original figure, the icosahedron. For this reason, the figure above is often called “the final stellation of the icosahedron,” as well as “the complete icosahedron.” Its faces are twenty irregular star enneagons, of the type shown below. The red areas are the “facelets” which can be seen, while the other parts of the star enneagon are hidden inside the figure.
Both of these images were made using Stella 4d: Polyhedron Navigator, which you can try for yourself right here. A free trial download is available.
RobertLovesPi.net 
I’m reading this on my phone and couldn’t see the figure until I scrolled down. I tried to figure out what I would see amd i as so far off. I didn’t expect the star-like points. Is there a simple explanation for why it’s not a “solid?”
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It’s one of the many polyhedra with faces which interpenetrate. The great dodecahedron is another, as are the great and small stellated dodecahedra. Is that what you mean by “not . . . ‘solid’?”
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Yeah, that’s what I meant! Dr. Pi, you could be my math teacher!!!
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Oh, that picture must require a flash player. Looking at it on my computer makes quite a difference!
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