1 op - [Null]
2n-1 op - Dual*
2n-1 op - Omnitruncation*
2n-1+1 op - Expansion*
*Only works on linear coxeter diagrams
2 op - Rectification
3 op - Truncation
4 op - Birectification
5 op - Cantellation
6 op - Bitruncation
7 op - Cantitruncation
8 op - Trirectification
9 op - Runcination
10 op - Bicantellation
11 op - Runcitruncation
12 op - Tritruncation
13 op - Runcicantellation
14 op - Bicantitruncation
15 op - Runcicantitruncation
16 op - Tetrarectification
17 op - Sterication
18 op - Biruncination
19 op - Steritruncation
20 op - Tricantellation
21 op - Stericantellation
22 op - Biruncitruncation
23 op - Stericantitruncation
24 op - Tetratruncation
25 op - Steriruncination
26 op - Biruncicantellation
27 op - Steriruncitruncation
28 op - Tricantitruncation
29 op - Steriruncicantellation
30 op - Biruncicantitruncation
31 op - Steriruncicantitruncation
32 op - Pentarectification
That's all I have time to write by hand. After 16 op or so they're useless anyway. Refer to the polytope wiki page on wythoffian operations for more information. I might write a program to generate higher ones, while writing this page I finally figured out how it works fully, and it's fairly simple for a human to do.
Their system works based off of rank expansions. Expanding edges is truncation, expanding faces is cantellation, expanding cells is runcination, and so on. When the CD starts with a ringed node, simply speak the expansion prefixes largest to smallest based off of the other ringed nodes. For example, xoxox has the fifth and third nodes ringed, so it'd be steri-cant-ellated. xxox has the second and fourth nodes ringed, so it'd be runci-trun-cated.
What if the CD doesn't start with a ringed node? Well, look for the first ringed node, and its position is the prefix and where to start from. So even though you might think ooxx is runcicanti something, because of the fourth and third nodes, it's actually called "tritruncation", because it starts on the third node, and then only has the second node ringed.
I'm not the biggest fan of this system. Now that I understand it, I like it a bit better, but it's overcomplicated, gets long quickly, and requires a lot of memorization. It's definitely one of the better polytope naming schemes that's popular, though.