Dear Ruud, I very much agree with your comment...
> Mathematically, a polyhedron ... need not be > regular or indeed convex. My favourite polyhedron is the Szilassi Torus. This is not just concave but, as the name implies, it is equivalent to a ring. This polyhedron has just SEVEN faces. Each face is an irregular hexagon. I find it remarkable that with just seven flat hexagonal faces you can make a torus. This polyhedron illustrates the Seven-Colour Map Problem: each face has an edge in common with each of the other six faces. Before you rush to Google, see if you can work out how such a torus is possible. I am certain you could make a sundial from a Szilassi Torus with one (or more) of its edges casting a shadow onto one (or more) of its faces There would be no need for vulnerable gnomons; the whole thing could be made out of stone. OK: that's my challenge for the week! Oh, I REALLY enjoyed your doggerel: > KonKAV ist eine Fläche dann, > wenn man KAFfee hineinschütten kann. I didn't know there were jokes like that in German! Does it translate into Dutch? Please send me more, but OFF List!! Frank H. King Cambridge, U.K. --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
