On the Twists of Listing and Tait

Thomas Penyngton Kirkman · Proceedings of the Royal Society of Edinburgh · 1885

In the figure 1 following, the knot 9 A j has a triangular section P rr cutting away on each side of it a (3 + r )-gonal mesh, and 9 A r 2 has such a section R pp , through one crossing only. Make in these knots creases at rr that approach to meet at R in 2, and creases pp that meet at P in 2. In 3, 2 is prepared for a rotation through two right angles about the fixed axis PE, through the crossing P and the crease-kiss R, or, as a more learned man would say, through the decussation P and the plicatorial osculation R–taking 2 for 9 A j : exchange here P and R if 2 is 9 A r 2 .

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