FTO: the Bencisco method
Centres and triples face by face, then L3T.
The FTO (face-turning octahedron) has eight triangular faces, each turning a third of a turn. Bencisco, the common speed method, builds the first centres and the corner-edge triples around them, then the last centres and the last bottom triple, and finishes with L3T: the last face's pieces and the centres of the faces that meet it at a corner. L3T's first look, PF (pair formation), sets up pairs on the last face; it is not in the database, because the engine cannot tell its cases apart: an algorithm for a PF case also leaves a valid next-look case from most others.
Notation (as on the LowCubes sheets, held with the last face F in front): U, F, R, L, D, B, BR and BL turn a face; Rw a face and the middle layer, Rs the middle layer alone, Ro the whole puzzle about R's axis, Rt, Lt and Ft the whole puzzle a quarter turn about a corner. S and H are the tutorial's sledge and hedge: S is Ro R' U R U' Ro', H is R U' R' U.
An L3T case: everything outside the last step is solved.
The FTO unfolded.