Part of Kirkman's table of all nonisomorphic knot and link projections (1884) with at the most ten crossings. From the left to the right, they are given the projections of knots and links: 3_{1} or 3 in Conway notation, 4_{1} (22), 4_{1}^{2} (4), 5_{1}^{2} (212), 5_{2} (32), 5_{1} (5), 6_{3} (2112), 6_{3}^{2} (222) (the first row), 6_{1}^{3} (2,2,2), 6'_{3}^{2} (222'), 3_{1}#3_{1} (3#3), 6_{2} (312), 6_{1} (42), 6_{2}^{2} (33), 6_{1}^{2} (6), 6_{2}^{3} (.1) (the second row). This table contains together knots and links, without separating them in disjoint classes according to the number of components. At the end of the table, is the first nontrivial basic polyhedron 6^{*} (.1) - the regular octahedron. The derivation principle - the addition of digons, could be seen from the Conway symbols of the linear and rational links belonging to this table: 3 22 4 212 32 5 2112 222 312 42 33 6 |