HKPLL
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HKPLL is an algorithm set that permutes the remaining 9 pieces (8 on the U layer and DF edge). Although invented as a substep of the Hawaiian Kociemba Method where it is preceded by HKOLL, it can also be used in Portico and Petrus-W.
The cases where only edges need to be permuted are called EHKPLLs. These are exactly the same as L5EP for DF and U layer edges.
There are currently no pictures of the cases yet (this is being worked on), but you can load them in Cube Explorer for a visual. They were generated by Brayden Mossey (wir3sandfir3s).
A more ergonomic Algorithm set of HKPLL has already been generated where instead of the DF edge being unsolved, the FR edge is unsolved. When using Hawaiian Kociemba you can change it so that you solve the DFr pair instead of the dFR pair to get this version of HKPLL.