Dang. I thought this would be about transgenders. -------- Original Message -------- Subject: [math-fun] Near misses Date: 2019-02-21 11:43 From: "Bernie Cosell" <bernie@fantasyfarm.com> To: math-fun@mailman.xmission.com Reply-To: math-fun <math-fun@mailman.xmission.com> < http://nautil.us/issue/69/patterns/the-impossible-mathematics-of-the-real-wo...
Bogus article. There are finitely many Johnson solids only because they're restricted to properly convex. Mathematica has them all (with unit edges. Might make a nice poster): In[28]:= PolyhedronData@"Johnson" Out[28]= {"AugmentedDodecahedron", "AugmentedHexagonalPrism", \ "AugmentedPentagonalPrism", "AugmentedSphenocorona", \ "AugmentedTriangularPrism", "AugmentedTridiminishedIcosahedron", \ "AugmentedTruncatedCube", "AugmentedTruncatedDodecahedron", \ "AugmentedTruncatedTetrahedron", "BiaugmentedPentagonalPrism", \ "BiaugmentedTriangularPrism", "BiaugmentedTruncatedCube", \ "BigyrateDiminishedRhombicosidodecahedron", "Bilunabirotunda", \ "DiminishedRhombicosidodecahedron", {"Dipyramid", 3}, {"Dipyramid", 5}, "Disphenocingulum", "ElongatedPentagonalCupola", \ "ElongatedPentagonalDipyramid", "ElongatedPentagonalGyrobicupola", \ "ElongatedPentagonalGyrobirotunda", \ "ElongatedPentagonalGyrocupolarotunda", \ "ElongatedPentagonalOrthobicupola", \ "ElongatedPentagonalOrthobirotunda", \ "ElongatedPentagonalOrthocupolarotunda", \ "ElongatedPentagonalPyramid", "ElongatedPentagonalRotunda", \ "ElongatedSquareCupola", "ElongatedSquareDipyramid", \ "ElongatedSquareGyrobicupola", "ElongatedSquarePyramid", \ "ElongatedTriangularCupola", "ElongatedTriangularDipyramid", \ "ElongatedTriangularGyrobicupola", \ "ElongatedTriangularOrthobicupola", "ElongatedTriangularPyramid", \ "GyrateBidiminishedRhombicosidodecahedron", \ "GyrateRhombicosidodecahedron", "Gyrobifastigium", \ "GyroelongatedPentagonalBicupola", \ "GyroelongatedPentagonalBirotunda", "GyroelongatedPentagonalCupola", \ "GyroelongatedPentagonalCupolarotunda", \ "GyroelongatedPentagonalPyramid", "GyroelongatedPentagonalRotunda", \ "GyroelongatedSquareBicupola", "GyroelongatedSquareCupola", \ "GyroelongatedSquareDipyramid", "GyroelongatedSquarePyramid", \ "GyroelongatedTriangularBicupola", "GyroelongatedTriangularCupola", \ "Hebesphenomegacorona", "MetabiaugmentedDodecahedron", \ "MetabiaugmentedHexagonalPrism", \ "MetabiaugmentedTruncatedDodecahedron", \ "MetabidiminishedIcosahedron", \ "MetabidiminishedRhombicosidodecahedron", \ "MetabigyrateRhombicosidodecahedron", \ "MetagyrateDiminishedRhombicosidodecahedron", \ "ParabiaugmentedDodecahedron", "ParabiaugmentedHexagonalPrism", \ "ParabiaugmentedTruncatedDodecahedron", \ "ParabidiminishedRhombicosidodecahedron", \ "ParabigyrateRhombicosidodecahedron", \ "ParagyrateDiminishedRhombicosidodecahedron", "PentagonalCupola", \ "PentagonalGyrobicupola", "PentagonalGyrocupolarotunda", \ "PentagonalOrthobicupola", "PentagonalOrthobirotunda", \ "PentagonalOrthocupolarotunda", "PentagonalRotunda", {"Pyramid", 4}, {"Pyramid", 5}, "SnubDisphenoid", "SnubSquareAntiprism", "Sphenocorona", \ "Sphenomegacorona", "SquareCupola", "SquareGyrobicupola", \ "SquareOrthobicupola", "TriangularCupola", \ "TriangularHebesphenorotunda", "TriangularOrthobicupola", \ "TriaugmentedDodecahedron", "TriaugmentedHexagonalPrism", \ "TriaugmentedTriangularPrism", "TriaugmentedTruncatedDodecahedron", \ "TridiminishedIcosahedron", "TridiminishedRhombicosidodecahedron", \ "TrigyrateRhombicosidodecahedron"} (The spelling corrector just had a coronary.) Speaking of wiggle room, does anyone remember a discussion we had where I offered a bogus counterexample in the form of a fanfolded, Möbius-looped strip? Were we discussing flexible polyhedra? —rwg /b\ Bernie Cosell bernie@fantasyfarm.com -- Too many people; too few sheep --