The Final Stellation of the Icosahedron

Stellated Icosa

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.

Stellated Icosa-StelDiag

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.

4 thoughts on “The Final Stellation of the Icosahedron

  1. 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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