  An embedding of chaotic data into a suitable phase space creates a
diffeomorphism of the original attractor with the reconstructed attractor.
Although diffeomorphic, the original and reconstructed attractors may not be
topologically equivalent. In a previous work we showed how the original and
reconstructed attractors can differ when the original is three-dimensional and
of genus-one type. In the present work we extend this result to
three-dimensional attractors of arbitrary genus. This result describes
symmetries exhibited by the Lorenz attractor and its reconstructions.
