Update – Nov 9, 2020
Françoise in Switzerland recently contacted me to ask how I made these braids, and I am pasting here my reply to her, in case it might help anyone else:

Odd rows:
The first row, and all the following “odd” rows of braiding are exactly like braiding a square braid – see the drawing further up this page. (A full ‘row’ is both main moves – first on the left hand and then on the right hand.)

Even rows:
On the even rows of braiding, the taken loop goes through the passive loops in a different orientation:

In the 2nd row, I insert my fetching finger in a ‘backward’ direction through each passive loop, as I send the finger on its way toward the loop it will fetch – the ‘active’ loop .

I go through those passive loops in the same order as usual, but each loop gets a half-twist because of the way I insert my fetching finger through it.

Then I take the furthest loop – the active loop – and bring it through all those ‘half-twisted’ passive loops. If the active loop is a single-color loop, it doesn’t matter whether you turn it or not. If it’s a bicolor loop, decide which color you want to be ‘up’, and then take the loop without turning it if the correct color is already ‘up’; but turn the loop if that color is ‘down’.

I do this same thing on both hands. (one ‘row’ or cycle of braiding)

Then in the 3rd row (an odd row) of braiding, I again put my finger through all the loops in the normal way, without twisting them (both on the left and the right side), just as I did in the 1st row of braiding.

(Etc., etc.)

Tightening:
The tightening move is very important for this braid. There must be a tightening move after each loop transfer – don’t wait until after the end of a row (both the left and right loop transfer) to tighten – especially when using many loops.

Compared to a square braid, there will be more resistance from the braid when you tighten, because of the twisted ‘passive’ loops in each row. Tighten firmly.

Bigger braids:
The resulting braid looks best if it has more than ten loops, but practice the technique first in a 5 to 9-loop braid. 5 and 7-loop braids aren’t big enough to result in repp-like rows (see the two 7-loop braids on the left in my photo). I’m not sure about 9 loops – I may not have tried that. Maybe 9 loops would be enough to show the nice repp rows, and doesn’t require holding more than one loop per finger.

See my 11- and 13-loop tutorial to learn how I handle extra loops when braiding a square braid. The same principles apply here with these repp braids.

Bicolor loops:
In the photo, the 3 braids in the center had (mostly) bicolor loops – the braids with zebra-stripes, rows alternately dark and light.

Because all the passive loops turn with each row, if you use bicolor loops and start braiding with the same color in upper position on all fingers, the result is one slanted row of dark followed by one row of light.

In those three braids, the steeper-slanting red or pink lines passing across the dark-light rows are formed by contrasting single-color loops, not bicolor. (Maybe 3 single-color loops in each braid, which must be set up on adjacent fingers).

The traditional way to make a braid that looks almost the same as any of these braids:

The braids that were often called bends or chevrons in the old loop braiding manuscripts are of twining, not plain weave, but they come out looking almost the same as my plain weave repp braids. Both types can be called ‘repp’ because of their bulging rows.

For the twined type of repp braid, before each loop transfer, you physically lift each passive “through” loop off the finger, turn it over, and replace it back on the finger. Then after all that, you pull the “active” outer loop through the passive loops.

You do this take-off-and-turn in every row of braiding, so these are rather slow to braid. The loops are continually turned in the same rotational direction on each side of the braid (though in opposite directions on the left and right hands), which is why the resulting physical structure is twining rather than plain weave.

The way I made the braids in my photo above, the passive ‘through’ loops are in effect temporarily turned in one direction on even rows, but then they automatically reverse back in the opposite direction during the following row (when I don’t turn them), cancelling out the preceding turn. The result is plain weave rather than twining. I stumbled onto this method first when using handheld loops and trying to reproduce ancient Andean plain weave repp braids. I found that with handheld loops you can turn them all in one direction on even rows, and in the opposite direction on odd rows to end up with plain weave. Much later this fun trick for doing it an even faster way with fingerloops came to me. (I think Masako Kinoshita or Noémi Speiser called this kind of sneaky move a ‘backward’ or ‘upside-down’ loop transfer? but I can’t remember now where I saw that reference.)

It’s faster than braiding the traditional twined braids called bends or chevrons, because I don’t have to take each passive loop off the finger, twist and replace, before the taken loop goes through them. And I don’t have to do anything ‘extra’ at all on the odd rows.

That doesn’t mean these braids are ‘better,’ btw! just faster to make. Twined braids may well be stronger than plain weave braids, for example – the two are actually very different structurally even if they can look superficially similar. I’m sure that 15th C. braiders would have called these bends and chevrons too, and many of them may well have used this same sneaky technique instead of the the full “turn, turn, turn” twining method that is described in the old manuscripts.