Enumeration of stellations (by Miller's rules)

For general discussion of polyhedra, not necessarily Stella-specific.
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robertw
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Enumeration of stellations (by Miller's rules)

Post by robertw » Mon Mar 03, 2008 8:02 am

Some of you may know the page where I list the number of stellations, by Miller's rules, for many of the Platonic/Archimedean solids:
http://www.software3d.com/Enumerate.php

Well, I got an email from Marc Newin, with a new result not presented in my table! A count for the number of reflexible stellations of the icosidodecahedron. The count was 7071672. I must have overlooked filling in this and a couple of other ones earlier, as sure enough, Stella comes to the same number in just 29 seconds. I had left them because the full count was unreachable (the count including chiral stellations), but setting "Options->Maintain Reflexibility" and performing the enumeration tells Stella to just count the reflexible stellations, and the count is done efficiently enough to make the result easily reachable.

So I have filled in this new value in my page above, along with a couple of others, the reflexible count for the truncated icosahedron (162782259) and the truncated dodecahedron (128761995).

I also filled in some more counts for prisms and antiprisms, for what it's worth :)

Rob.

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