It is also possible to have convex (as well as non-convex) dodecahedra with all faces congruent non-regular pentagons. One can even make them with all vertices rational points in R^3. I think the faces can be equilateral as well, but it has been so long since I looked at this, I'd have to check that part. Jim Buddenhagen On Mon, Aug 8, 2011 at 5:37 AM, Bill Gosper <billgosper@gmail.com> wrote:
Julian flew back from math camp today (on one hr's sleep) and, generalizing a question of mine, found a dodecahedron with (planar) equilateral pentagonal faces, but not the usual ones. Before peeking <http://gosper.org/dodohedron.png>, you might try to find one. After peeking, please speak up if you've seen it before. Tnx, --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun