clsn@Dranorter Well, "identical sides" should include the nature of the corners and edges around them. You are correct that just having congruent faces isn't enough. But Catalan solids are "face-transitive", meaning that they're essentially symmetrical with respect to their faces: each face (and its bordering edges/vertices/neighboring faces) is indistinguishable from the others, and that's really what you need to be a fair die (well, a sufficient but not necessary condition; see loki3's lovely counterexample http://shpws.me/HHbd)
clsn It does work and is actually pretty cool. I'm not all that organized to begin with, maybe it isn't as useful to me as it might be to others, but it is fun to carry around and know you have $1.50 in quarters just in case...
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