...this base mat is highly symmetric, more symmetric than the Diamond knot that can be derived from it.
Noope !
It is more symmetric than
some Diamond knots that can be derived from it ( as the globular
Diamond loop, where three limbs are loaded ), but it is
not more symmetric than others ( as the two planar, face symmetric
Diamond bends, where two limbs are loaded ). It is the mat, the "
theoretical" knot, the knot which should be considered as the base knot. This knot is symmetric, albeit less symmetric than the
Tweedledee knot, indeed - which is "
triply symmetric" ( according to the nomenclature established by Miles ).
Now, this symmetric mat can be loaded symmetrically, i.e., by two or four limbs, and generate symmetric knots, or asymmetrically, i.e., by three limbs, and generate asymmetric knot,
as it should have been expected ! The
Tweedledee loop is also asymmetrically loaded, but there the geometrical distortion of the base knot, the Tweedledee mat, is not so pronounced and visible, and it may even be unnoticed. In the case of the Diamond mat, the asymmetric loading ( by three limbs ) forces the nub to curl, and finally settle in this globular form of the
Diamond loop. We should not be fooled by the stability of some loop knots, as the
Tweedledee bowline ( or, for that matter, of the fake, so-called "Zeppelin loop" ), and believe that they are symmetric... They are not. Eventually, under heavy loading, this asymmetry will be manifested. In the case of the Diamond knot, it happens that the parent Diamond mat is very unstable, and sensitive to the asymmetric, three-limbs loading, and takes this globular form immediately, even under a light loading.
What I have pointed out is that, usually, one does not go to the knot of bend starting from the knot of the loop, but starting from the knot of the mat. If you follow this sequence, you will never arrive at the globular form of the knot of the loop, and use it as a bend !
...the level of symmetry of the Diamond knot... is lower than that for example of the Tweedledee knot.
Right. However, that does not mean that the
Diamond knot is a-symmetric !
... the bend shown at reply #13, with that geometry, is not symmetric like the Tweedledee bend ...[it] has no hope of being symmetrically loaded,
Right. Now I understand what you are saying... Therefore you have to derive the two face-symmetric bends from the mat, not from the loop. The correct sequence is : mat ---> bends ---> loop,
not mat ---> loop ---> bend.
...the bend that you will obtain... is not even remotely similar to the Diamond bend that you show at reply #13.
Correct. The label of the picture in Reply#13 is misleading. I should had labelled it as " Diamond loop ( detail )". It is a good thing to have a knot-tyer-angel who saves you from those mistakes !