Hello, forgive my naive thoughts, but wouldn't the argument used in the article of wavelengths needing to fit in the space (don't even know if this is a commonly agreed one, even if it sounds plausible) prevent non-orientable finite spaces at all? At least, it would only allow an uneven number of zero-crossings of a wave, whereas an orientable finite space allows only an even number? Could this be astronomically observed somehow? (Just tried to draw some waves on a moebius band) Greetings, Dirk Lattermann [...] Boy, I'd be delighted if the universe were a Poicare Dodecahedron! (Though I'd been hoping for a nonorientable space: if Weeks is right, then you could go in a straight line for 74 billion light-years and get back to where you started, just rotated by 2pi/5. I'd been hoping you'd get back to where you started mirror imaged.) --Michael Kleber kleber@brandeis.edu _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun