The Perko pair is a pair of knot diagrams which can be found in the
early knot tables. Subsequently the two diagrams were shown to
represent the same knot. You may come across as many as three
different versions of the Perko pair in the literature. This is
because after the early tables were created subsequent authors
reproduced them using different diagrams. Here is Perko's isotopy from
10_{5II} to 10_{6VI} as they appeared in the early
tables.
If you have access to JSTOR Perko's paper can be found here
Kenneth A. Perko, Jr. Proceedings of the American Mathematical Society, Vol. 45,
No. 2. (Aug., 1974), pp. 262-266.