In practical knotting, the word "flype" means to shift and transpose a collar alongside a knot, from the one side of it to the other, without any involvement of the sides themselves ( that is, without first pulling the collar out of the knot from the one side, in order to turn it into a "free" bight which does not encircle the knot any more, then flip this bight 180 degrees, and finally push the other side of the knot into it, in order to turn the bight into a collar again. So, a "flype" can be performed even if the ends of a knot are inaccessible ). In the case of a loop, this means to transform a collar around the eye legs, to a collar around the Standing and Tail Ends, as shown in the first attached picture ( copied from an article by Harry Asher, Knotting Matters 29 ). Notice that in this transformation the eye of the loop, or the pair of the Standing and Tail Ends, is not involved, i.e., these ends are not tucked in or out of the collar. In the case of a fig.8 knot, to flype it ( verb) or a flype on/of it ( noun ), is equivalent to the transformation shown by Desmond Mandeville in Knotting Matters 23, and copied here in the second attached picture. The collar at the left side is transposed at the right side , and vive versa. The topology of the knot is not altered at any stage - it is just its geometry that changes, from a fig.8 knot, through an intermediate Pretzel-like knot, to another fig.8 knot. ( However, the number of crossings does change, but that has to do only with the representation of the knot on 2D, not with its topology in 3D. )
This transformation is helpful when we want to transpose a collar in a eye-knot which collars the eye legs, to a more "proper" location, around the Standing End - because the nub of a eye-knot with a collar around its eye legs may suffer a severe deformation when the eye will be ring-loaded.
