
To make the polyhedron shown above, I started with an icosahedron . . .

. . . and then I augmented each face with a triangular cupola, with this polyhedron’s hexagonal faces pointed outward.

I made these images using Stella 4d, which you can try for free at this website.
This reminds me of something I came across which I bookmarked:
http://www.matematicasvisuales.com/english/html/geometry/resources/rubberbands.html
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