The polyhedra shown above and below are duals. The one above has 1800 faces and 960 vertices. The one below has 960 faces, and 1800 vertices. This “flipping” of the face and vertex numbers always happens with dual polyhedra.
Also, two dual polyhedra always have the same number of edges, which can be found by subtracting two from the sum of the numbers of faces and vertices (this is based on Euler’s Formula, F + V = E + 2). In this case, each of these polyhedra have 1800 + 960 – 2 = 2758 edges.
These virtual models were created using Stella 4d: Polyhedron Navigator, software you can try for yourself right here.
[Later note: I have noticed a lot of referrals to this post through stumbleupon.com, and wish to thank the unknown person who posted the link there for all this increased traffic to my blog. To those who are finding me via StumbleUpon, welcome! I invite you to check out other posts here, as well. The “topic cloud” on the right side of the page should help you find stuff of interest to you, of the 1000+ posts here, many of which are also about polyhedra.]
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Is there a function for making these?
There are mathematical functions related to polyhedra — but I don’t think one exists for making them, although I could be wrong.
There does exist high-quality software for manipulating polyhedra and making these images, though, and it even has a free trial download available. The website to visit for this is http://www.software3d.com/Stella.php — and, of the options available, Stella 4d is the one I recommend.
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