Johnson chose to enumerate Regular-faced Aplanar Convex (RAC) polyhedra pretty much exactly because it was a finite class that wasn't too hard to cover methodically. Allowing flat or concave dihedrals creates infinite classes about which it's hard to say much. Are you asking what the largest dihedral would be in these classes? Obviously pi for flat dihedrals; my vague intuition is "no upper bound" for concave dihedrals, but I have only about 60% confidence in that answer. On Sun, Oct 28, 2018 at 11:50 PM Bill Gosper <billgosper@gmail.com> wrote:

Mathematica knows all 92. (Regular polygonal faces, dihedrals < π, not ordinary prisms.) Name any of the four with largest dihedral. According to ries, that angle satisfies sinpi(sin(x)) = cospi(1/sqrt(6)).! —rwg Spoiler: (Kids: Don't peek! This is a nice exercise.) StringReverse@"]&]]\"selgnAlardehiD\",#[ataDnordehyloP[xaM@N ,][ataDnordehyloP[yBlamixaM@/&]#,#@ataDnordehyloP[delebaL" —rwg Gotcha: Why does this fail without the N@? Easy questions: Why disallow dihedrals > π (concavities)? Invisible edges with dihedral = π? _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun