For n = 5, the seven chord diagrams are given in the following table:
For n = 6, thirty three such diagrams and their corresponding selfavoiding curves given by mirror placements are illustrated in the corresponding figure. Different shadows of the same KL can give different selfavoiding curves, as in the case of the link 2 2 2. Visual recognition of selfavoiding curves, either direct or from shapes, is complicated even for a small number of mirrors, but it is almost immediate from chord diagrams. It is interesting to mention a possible connection between shapes originating from selfavoiding curves and some biological forms. From every KL shadow can be derived one or several selfavoiding curves. Some conclusions about original KLs can be made based on the chord diagrams of those selfavoiding curves. For example, to every diagonal connecting two vertices separated by one vertex, and to every pair of parallel adjacent diagonals corresponds a digon in the original KL shadow; diagrams without them correspond to basic polyhedra. This way, we can follow a process of bigon collapsing directly in chord diagrams. Among all chord diagrams, we can distinguish antisymmetrical diagrams, that remain unchanged by opposite coloring of chords. With regard to selfavoiding curves, this means that the external region is equal to the internal one. Such diagrams are selfdual. For example, for n = 6, eleven among 33 chord diagrams are selfdual. Again, families of KLs play important role as before, followed by families of chord diagrams and selfavoiding curves derived from them. Chord diagrams belonging to a same family can be visually recognized. Selfavoiding curves can be embedded on different surfaces, so together with Viae Globi on a sphere S^{3}, we can consider Viae Tori on a torus (later introduced in analogy to Sequin's Viae Globi), or on any other surface. The LinKnot function fDiffViae (webMathematica fDiffViae) for a given number n derives all different selfavoiding curves with n mirrors that can be obtained from prime KLs with n crossings. For every such curve given by its (uncolored) chord diagram we can find its basic prime KL by using the LinKnot function fViaToKL (webMathematica fViaToKL).
