Using “diamonds” to reduce the number of edges is very common in organic modelling. The attached pic is of the hand of a Daz 3D figure - possibly the best commercially available figures animatable figures. In this case it is used to reduce the number of edges in the hand from flowing into the arm, where they would be redundant.
What you do is merge 3 verts, which results in a triangle - dissolve the line down the centre of the triangle to form a quad and pull one of the verts to form the diamond shape.
The “diamond/losange” technique is used to lose 2 vertices , you can’t lose only 1 with it
by example :
5 vertices, and after the diamond/losange technique :
3 vertices are left
So you can go from 3 to 1 but not from 3 to 2 if you want to use that technique.
Even the other method :
Still lose 2 vertices, not 1 at once
If you want to only lose 1 (and of course keep all quads, as you could just go the easy and painless way and admit a triangle in your model (no shame in that even professionals do that for their quality game assets), you’ll be forced to add a loop cut somewhere or remove a loop cut.in the hand or arm
If it was my model, i would add a loop cut to the arm if i can’t remove one in the hand
And then rework the spacing in the arm
The problem is in fact exactly the same as trying to change a ngon made of uneven amount of vertices ( 5 / 7 / 9 / etc…) into quads.
You will always have to add a loop cut in order to make the ngon having an even amount of faces ( 6 / 8 / 10 / etc…) in which case, you can transform it into quads.
If you don’t , you’ll have to have a triangle
I fully agree with Sanctuary as far as using that method to cut down from 3 to 1. The problem with adding redundant loop cuts in the arm is that it tends to square the arm. In the second pic Composer ends up having what looks like a long thin triangle running up the arm - that is definitely not a good result and that is what needs to be sorted out by merging them. That way he will end up with one loop instead of three.