I had tied and tried the
**10 hitch, and all the other hitches I could derive from the Borromenean rings. No good practical knot emerged. It seems that Mathematical "knots" can rarely, only, serve as an inspiration for Practical knots - because the most important characteristic of the former is topology, while of the later is geometry - and there is no bridge in between those two Lands.
In Practical knots, we start from one of the few geometrical configurations, which is stable
because it utilizes the friction of ropes - we do not start from one of the many topological configurations of the Mathematical "knots", which will become stable knot
if it utilizes ropes with friction.
Many of the best Practical knots I know are TIB, that is, topologically equivalent to the un-"knot", to the un-"knotted" line. What could emerge if one would had tried to figure out Practical knots starting from the mental image of an unknotted line ?
( Tie the
Double Cow hitch, or the
TackleClamp hitch shown in the attached pictures, which are based on the implementation of the
opposing bights locking mechanism, to see what I mean. )