So Platonic solids have five members, Archimedean Solids have 13. I was wondering if there was any notable and/or famous set of polyhedra that either has precisely 16 or, if that is not possible, then $2^n$ members.
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The sets should be interesting for what they are, not for how many elements are in them. – Ivan Neretin Jan 29 '20 at 14:15
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I am aware. I Just asked whether some set happens to fulfill this particular and arbitrary property about its cardinality. – urquiza Jan 29 '20 at 14:18
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Why, many do. You may take a basket and grab the first 16 polyhedra you'll see, that will be a set all right. Whether it will have anything interesting about it, though, is hard to tell. Chances are it won't. – Ivan Neretin Jan 29 '20 at 14:22
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That is the very reason why I asked about a notable set of polyhedra. That is, a set that is famous and important for other particularities but just so happen to have such amount of members. – urquiza Jan 29 '20 at 14:45
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Oh wait, I didn't notice the word "notable" in the title, sorry about that. Well, I don't know of such family off the top of my head. There are 32 crystallographic point groups, but these are not quite the same as polyhedra (though not entirely unrelated either). – Ivan Neretin Jan 29 '20 at 15:00
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That is fine. I just realized that even though the word "notable" is present um the title, it does not show in the body of the question. So I will l edit it. – urquiza Jan 29 '20 at 15:19