2 VISUALIZING AMPHICHEIRALITY
In the case of rational knots, all amphicheiral knots are derived from the same source: from the figure-eight knot 2 2 (or 41 in the classic notation). The amphicheirality of the figure-eight knot can be visualized by an animation consisting from a series of ambient isotopies transforming a “left” figure-eight knot to the “right”. |
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For the knot 2 2, the graph symmetry group is G = [2+, 4], and the knot symmetry group G' = [2+, 4+] is generated by the rotational reflection, with the axis defined by the midpoints of colored (i.e., double) edges of the tetrahedron . | |||||
Considering the sign of the vertices, it is a rotational antireflection. Its effect is preserved in all rational knots with an even number of crossings that have a symmetrical Conway symbol. As the result, we obtain a series of centro-antisymmetrical graphs corresponding to rational knots. |
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