Consider the following graph in 3-space: Start with a white rectangle, say [0,3] x [0,1]. Blacken the intervals {n} x [0,1] for n = 0, 1, 2, 3. Also blacken the edges {0} x [0,1} and {1} x [0,1]. Now identify (0,t) with (1,1-t) for all t in [0,1], et voilà: a Möbius band. Arrange this in space to be the usual picture of a Möbius band with one half-twist. Finally, delete everything that is not blackened, leaving a graph of 6 edges and 6 vertices with a particular embedding in 3-space. Call the abstract graph K, and its embedding in space the function h: K -> R^3. PUZZLE: ------- Can K be continuously manipulated through homeomorphic graphs in 3-space so that it coincides with its mirror image? (Or more formally: Is there a continuous mapping H: K x [0,1] -> R^3 such that a) H(x,0) = h(x), for all x in K; b) H restricted to K x {t} is an embedding into R^3, for all t in [0,1]; c) H restricted to K x {1} is an embedding into R^3 whose image is a mirror image K' of K ?) --Dan