A couple of years ago, I was perusing my copy of *Ashley's Book of Knots* and came across the following passages:

"Many bends in common use may be tied on the Carrick Bend diagram" (ABoK 1545). As examples, Ashley gave diagrams for the Reef Knot (1549), Sheet Bend (1550), Carrick Bend (1551), and Granny Knot (1552).

"In a knot of eight crossings, which is about the average-size knot, there are 256 different 'over-and-under' arrangements possible... Make only one change in this 'over-and-under' sequence and either an entirely different knot is made or no knot at all may result". Ashley gave illustrations for the Reef Knot (77), Sheet Bend (78), and no knot (79).

That got me to wondering just how many bends there are in the Carrick form, and were any of them new. Disregarding the lead (as in the Josephine Knot) the Carrick diagram has eight crossings, and as Ashley observed, there are potentially 256 over/under combinations (see the first image below). Add to that, however, that (as a bend), the standing ends may be either on diagonally opposite sides (see image 2) or on the same side (see image 3), and you get a total of 512 possible bends (1024 if you entertain all possible lead combinations, but rotational symmetry allows us to discard half of them).

Being both curious and methodical, I decided to tie them all and find out.