here are the cases for the last two sets of tredges, split into cases with/without the parity
no parity
simple match/flip  
d R U R' F R' F' R d'  d' L' U' L F' L F L' d 


this is the same case, just mirrored. it is probably the best and easiest case to end up with, and the easiest to understand. the idea is join the matching wing and edge (with the first d/d' turn) then take the edge out, and reinsert it upside down, then the unfold (last d/d') brings the final piece back into position and restores centers. 
double wing swaps  
u2 r2 F2 u2 U2 F2 r2 u2  F2 r D2 r' F2 U2 F2 l B2 l' 


this first case will swap two wings on one side, for the ones directly across while preserving orientation, the second alg swaps the same pieces, but flips orientation. The first alg is easier done for me with edges on FL and FR, while the second is easier with them on UF and UB, be sure to experiment with algs to see what works best for you. 
double edge flip 
u' d R U R' F R' F' R d' u 

This will flip two middle edges, same idea as the simple match/flip, except the centers are moved over instead of a wing. take it out, flip it upside down, put it back and restore. This is a good final case to get, also, using E/E' on the first turn is possible instead of slicing. 
with parity
single edge flip 
r2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 r2 

this is the single parity. it is similar to the revenge parity and the same alg can be used. There are a couple of algs for this case, but this one seems to be the most popular. you can usually avoid this case by itself with a good look ahead and instead get one of the easier parity situations. like the 4x4, there are faster execution algs to get rid of the parity, this alg is typically used only when you have all 11 other tredges completed with this left over. you can maintain top face orientation by doing inner ring cuts only for the deep slices, again like the 4x4 OLL parity algs. 
double parity 
r2 B2 r' U2 r' U2 B2 r' B2 r B2 r' B2 r2 

this is a just like the double parity alg on revenge, it swaps the two groups of wings like the double wing swap, but it also flips one edge. this is also a popular alg to get rid of the parity if you notice you have it with more than 2 edge groups left. 
edge flip/swap 
l' U2 l' U2 F2 l' F2 r U2 r' U2 l2 

this parity is similar looking to the last two edges on revenge, just one side is a double. this will swap and flip the two remaining wings. 
checkerboard  
l U2 l2 U2 l' U2 l U2 l' U2 l2 U2 l  r' U2 r2 U2 r U2 r' U2 r U2 r2 U2 r' 


these patterns are easy to recognize since nothing is matched up, and the algs for them are also easy, usually faster than the single parity execution for me. 
these cases are all the final edge configurations for the last two tredges, you don't need them all to be able to solve the 5x5 everytime, but its good to eventually learn them all. if you're looking at a minimum to learn, the recommended repotoire is single match/swap (and learn the double center flip at the same time, since its the same alg, just with a different starting and finishing move), regular double wing swap, single edge parity. after that the double parity, edge flip/swap and checkboards. finally the double wing swap/flip since it is the rarest case. these cases can sometimes be applied to individual groups in the last four to fix a tredge, however, regular pairing up as shown on the edges page requires many less moves than these cases. with some experimentation and practice the last four tredges can be pretty quick, and a great time to look ahead for the start of the 3x3 phase.
other useful algs and ideas
these next algs are useful for advanced last four edges strategies, one flips three centers (the ones at FU, FD, and BD). this alg can also fix the parity since it flips an odd number of centers.
the other is a simple M' U M idea, but when nothing good is visible to start with on the last four tredges, often that sequence will make an easy start somewhere. note that it create an edge threecycle, and swaps the BU and BD wings. at first it will be hard to see where to apply it for best results, it will usually do something good if you just randomly apply it, after time the best cycle will become more apparent.
flip 3 edges  cycle edges and swap wings 
r U2 l' U2 F2 r U2 l2 B2 l' B2 l F2 D2 l2  l r' U2 l' r 


master final edges  <15  there is no transitional delay between the first eight and last four edges, multiple pieces are placed at once 
intermediate final edges  <30  sluggish finding the best way to finish, usually the technique is ok, but the look ahead is what needs the work 
beginner final edges  30+  its difficult to see what to pair up, and sometimes you undo previous matches accidently while pairing something up. practice is the key 
©20052023 frank morris & clancy cochran