The Figure Eight Knot

The Figure Eight Knot may look chiral but it is achiral. For a dynamic view, click here. Chiral compounds are not superimposable on their mirror images. If the figure 8 knot (upper left) is rotated about the x-axis, knot 2 is produced. Unlike Alice going through the Looking Glass, one can go from knot 1 to 2 by rotation about the axes. Rotation of knot 1 about the x-axis produces knot 3, which is identical to knot 2, proving that knot 2 is not a mirror image. Rotation of knot 2 or 3 about the y-axis produces knot 4. Thus, knots 1-4 are all identical or superimposable on one another.


The figure 8 knot has a center of symmetry (lower left). Any point on the rope has a corresponding point that can be connected by the dotted red line. The intersection of these lines is the center of symmetry. In meso tartaric acid, the anti conformation also has a center of symmetry. The eclipsed conformation of meso tartaric acid that has a dihedral angle of 0o for the same group has a plane of symmetry. These two conformations are achiral by internal comparison. Every other conformation, staggered or eclipsed, of meso tartaric acid has a mirror image that can be formed by rotation about the C2-C3 bond. Meso tartaric acid is achiral!