[math-fun] Julian's dodecahedron
is made by replacing ten of the regular pentagons of a dodecahedron with concave equilateral pentagons, preserving the topology: http://gosper.org/dodohedron.png ( !#%&*@! was deleted again. Apologies to any of you who looked for it.) http://en.wikipedia.org/wiki/Dodecahedron glaringly omits it: [...] Topologically distinct dodecahedra include: - Pentagonal dodecahedra: - Regular dodecahedron, 12 pentagonal faces, Ih<http://en.wikipedia.org/wiki/Icosahedral_symmetry>symmetry, order 120 - Pentagonal truncated trapezohedron<http://en.wikipedia.org/wiki/Truncated_trapezohedron>- same topology as regular form, but D5d <http://en.wikipedia.org/wiki/Dihedral_symmetry> symmetry, order 20 - "Pyritohedron <http://en.wikipedia.org/wiki/Pyritohedron>" - same topology as regular form, but Th<http://en.wikipedia.org/wiki/Tetrahedral_symmetry>symmetry, order 12 - Uniform polyhedra: - Decagonal prism <http://en.wikipedia.org/wiki/Decagonal_prism> – 10 squares, 2 decagons, D10h<http://en.wikipedia.org/wiki/Dihedral_symmetry>symmetry, order 40 - Pentagonal antiprism<http://en.wikipedia.org/wiki/Pentagonal_antiprism>– 10 equilateral triangles, 2 pentagons, D5d <http://en.wikipedia.org/wiki/Dihedral_symmetry> symmetry, order 20 - Johnson solids <http://en.wikipedia.org/wiki/Johnson_solid> (regular faced): - Pentagonal cupola <http://en.wikipedia.org/wiki/Pentagonal_cupola>– 5 triangles, 5 squares, 1 pentagon, 1 decagon, C5v <http://en.wikipedia.org/wiki/Cyclic_symmetry> symmetry, order 10 [...] reinforcing the suspicion that Julian was not anticipated. (Perhaps a contributing factor to the news not reaching Wikipedia was its repeated disappearance from my site.) Anyway, each of the three pentagonal dodecahedra has its own article, as well as mention in the above list. Obviously there should be an article on Julian's. (Julian, do you still have the coordinates?) It would be amusing to create the article, and watch the Wikiwardens delete it as Original Research. Do we really need to create Propp's Electronic Journal of Unoriginal Research? Even if those <PEJURative> Wikiwardens relented, we still have the problem of naming this solid! --rwg
Taking that idea one step backwards: "the drum" ? --Dan On 2013-09-01, at 11:27 AM, Marc LeBrun wrote:
="Bill Gosper" <billgosper@gmail.com> we still have the problem of naming this solid!
tympanon
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participants (3)
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Bill Gosper -
Dan Asimov -
Marc LeBrun