Since there's only one embedding of a circle in R^3 up to homotopy, there's an embedding of a mobius strip in R^3 where the edge is a geometric perfect circle. But I find myself unable to visualize such a thing. Has anyone seen a 3-d model of this surface? Second-best thing would be a graphic of such a thing, preferably one that you could rotate in 3 dimensions. I'd also like to better visualize Boy's surface, or any other immersion of RP^2 in R^3. It would also be interesting to have an insight into why immersing a Klein bottle in R^3 is easy, while immersing RP2 is "hard". I don't know of any formal sense in which this is true, but apparently Boy came up with this surface when challenged by Hilbert to prove that immersing RP^2 in R^3 was impossible. Also, are these two questions related? That is, can you immerse a mobius strip in R^3 in such a way that the boundary is a geometric circle, and that the union of this mobius strip and a disk with the same boundary is still an immersion (of RP^2 in R^3)? Andy Latto andy.latto@pobox.com -- Andy.Latto@pobox.com